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  • 1.
    Abrahamsson, Linda
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Statistical models of breast cancer tumour growth for mammography screening data2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 2.
    Abrahamsson, Per Anders
    et al.
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science. Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Adami, Hans Olov
    Taube, Adam
    Kim, KyungMann
    Zelen, Marvin
    Kulldorff, Martin
    Re: Long-term survival and mortality in prostate cancer treated with noncurative intent1995In: UROLGY, Vol. 154, p. 460-465Article in journal (Refereed)
  • 3.
    Achcar, JA
    et al.
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Agrawal, MC
    Anand, KN
    Ali, MM
    Ali, MM
    Bagui, SC
    Baker, RD
    Balamurali, S
    Balasooriya, U
    Bansal, AK
    Barry, J
    Bonett, DG
    Box, G
    Carling, K
    Caudill, SB
    Chakraborti, S
    Chatfield, C
    Chatterjee, S
    Cornell, JA
    Cox, D
    Draper, NR
    Ehrenberg, A
    Finney, DJ
    25 years of applied statistics1998In: JOURNAL OF APPLIED STATISTICS, ISSN 0266-4763, Vol. 25, no 1, p. 3-22Article in journal (Refereed)
  • 4. Adami, Hans-Olov
    et al.
    Bergström, Reinhold
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Weiderpass, Elisabete
    Persson, Ingemar
    Barlow, Lotti
    McLaughlin, Joseph K.
    Risk for endometrial cancer following breast cancer: A prospective study in Sweden1997In: Cancer Causes & Control, Vol. 8, p. 821-827Article in journal (Refereed)
  • 5. Adami, H-O
    et al.
    Bergström, R
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Engholm, G
    Nyrén, O
    Wolk, A
    Ekbom, A
    Englund, A
    Baron, J
    A prospective study of smoking and risk of prostate cancer1996In: Int J Cancer, Vol. 67, p. 764-768Article in journal (Refereed)
  • 6.
    Adami, J
    et al.
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Nyren, O
    Bergstrom, R
    Ekbom, A
    McLaughlin, JK
    Hogman, C
    Fraumeni, JF
    Glimelius, B
    Blood transfusion and non-Hodgkin lymphoma: Lack of association1997In: ANNALS OF INTERNAL MEDICINE, ISSN 0003-4819, Vol. 127, no 5, p. 365-&Article in journal (Refereed)
  • 7.
    Adriansson, Nils
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Mattsson, Ingrid
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Forecasting GDP Growth, or How Can Random Forests Improve Predictions in Economics?2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    GDP is used to measure the economic state of a country and accurate forecasts of it is therefore important. Using the Economic Tendency Survey we investigate forecasting quarterly GDP growth using the data mining technique Random Forest. Comparisons are made with a benchmark AR(1) and an ad hoc linear model built on the most important variables suggested by the Random Forest. Evaluation by forecasting shows that the Random Forest makes the most accurate forecast supporting the theory that there are benefits to using Random Forests on economic time series. 

  • 8.
    Ahlberg, Daniel
    et al.
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.
    Deijfen, Maria
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Competing first passage percolation on random graphs with finite variance degrees2019In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 55, no 3, p. 545-559Article in journal (Refereed)
    Abstract [en]

    We study the growth of two competing infection types on graphs generated by the configuration model with a given degree sequence. Starting from two vertices chosen uniformly at random, the infection types spread via the edges in the graph in that an uninfected vertex becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of nearest neighbors of type 1 (2). Assuming (essentially) that the degree of a randomly chosen vertex has finite second moment, we show that if lambda(1) = lambda(2), then the fraction of vertices that are ultimately infected by type 1 converges to a continuous random variable V is an element of (0,1), as the number of vertices tends to infinity. Both infection types hence occupy a positive (random) fraction of the vertices. If lambda(1) not equal lambda(2), on the other hand, then the type with the larger intensity occupies all but a vanishing fraction of the vertices. Our results apply also to a uniformly chosen simple graph with the given degree sequence.

  • 9.
    Ahlberg, Daniel
    et al.
    Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
    Griffiths, Simon
    PUC Rio, Dept Matemat, BR-22451900 Gavea, RJ, Brazil.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Morris, Robert
    Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
    Competition in growth and urns2019In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 54, no 2, p. 211-227Article in journal (Refereed)
    Abstract [en]

    We study survival among two competing types in two settings: a planar growth model related to two-neighbor bootstrap percolation, and a system of urns with graph-based interactions. In the planar growth model, uncolored sites are given a color at rate 0, 1 or infinity, depending on whether they have zero, one, or at least two neighbors of that color. In the urn scheme, each vertex of a graph G has an associated urn containing some number of either blue or red balls ( but not both). At each time step, a ball is chosen uniformly at random from all those currently present in the system, a ball of the same color is added to each neighboring urn, and balls in the same urn but of different colors annihilate on a one-for-one basis. We show that, for every connected graph G and every initial configuration, only one color survives almost surely. As a corollary, we deduce that in the two-type growth model on Z(2), one of the colors only infects a finite number of sites with probability one. We also discuss generalizations to higher dimensions and multi-type processes, and list a number of open problems and conjectures.

  • 10.
    Ahlberg, Daniel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Inst Nacl Matemat Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.;Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden..
    Steif, Jeffrey E.
    Univ Gothenburg, Chalmers Univ Technol, Math Sci, SE-41296 Gothenburg, Sweden..
    Pete, Gabor
    Hungarian Acad Sci, Renyi Inst, 13-15 Realtanoda U, H-1053 Budapest, Hungary.;Budapest Univ Technol & Econ, Inst Math, 1 Egry Jozsef U, H-1111 Budapest, Hungary..
    Scaling limits for the threshold window: When does a monotone Boolean function flip its outcome?2017In: Annales de l'I.H.P. Probabilites et statistiques, ISSN 0246-0203, E-ISSN 1778-7017, Vol. 53, no 4, p. 2135-2161Article in journal (Refereed)
    Abstract [en]

    Consider a monotone Boolean function f : {0, 1}(n) -> {0, 1} and the canonical monotone coupling {eta(p) : p is an element of [0, 1]} of an element in {0, 1}(n) chosen according to product measure with intensity p is an element of [0, 1]. The random point p is an element of [0, 1] where f (eta(p)) flips from 0 to 1 is often concentrated near a particular point, thus exhibiting a threshold phenomenon. For a sequence of such Boolean functions, we peer closely into this threshold window and consider, for large n, the limiting distribution (properly normalized to be nondegenerate) of this random point where the Boolean function switches from being 0 to 1. We determine this distribution for a number of the Boolean functions which are typically studied and pay particular attention to the functions corresponding to iterated majority and percolation crossings. It turns out that these limiting distributions have quite varying behavior. In fact, we show that any nondegenerate probability measure on R arises in this way for some sequence of Boolean functions.

  • 11.
    Ahlberg, Daniel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
    Tassion, Vincent
    Univ Geneva, 2-4 Rue Lievre, CH-1211 Geneva, Switzerland.
    Teixeira, Augusto
    Inst Matematica Pura & Aplicada, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil.
    Sharpness of the phase transition for continuum percolation in R22018In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 172, no 1-2, p. 525-581Article in journal (Refereed)
    Abstract [en]

    We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii are uniformly bounded from above. In this article, we investigate this process for unbounded (and possibly heavy tailed) radii distributions. Under mild assumptions on the radius distribution, we show that both the vacant and occupied sets undergo a phase transition at the same critical parameter.c. Moreover, For. <.c, the vacant set has a unique unbounded connected component and we give precise bounds on the one-arm probability for the occupied set, depending on the radius distribution. At criticality, we establish the box-crossing property, implying that no unbounded component can be found, neither in the occupied nor the vacant sets. We provide a polynomial decay for the probability of the one-arm events, under sharp conditions on the distribution of the radius. For. >.c, the occupied set has a unique unbounded component and we prove that the one-arm probability for the vacant decays exponentially fast. The techniques we develop in this article can be applied to other models such as the Poisson Voronoi and confetti percolation.

  • 12.
    Ahlberg, Daniel
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Inst Nacl Matemat Pura & Aplicada, Rio De Janeiro, RJ, Brazil;Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden;Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
    Tykesson, Johan
    Chalmers Univ Technol, Dept Math, SE-41296 Gothenburg, Sweden;Univ Gothenburg, Gothenburg, Sweden.
    Gilbert´s disc model with geostatical marking2018In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 50, no 4, p. 1075-1094Article in journal (Refereed)
    Abstract [en]

    We study a variant of Gilbert's disc model, in which discs are positioned at the points of a Poisson process in R-2 with radii determined by an underlying stationary and ergodic random field phi: R-2 -> [0, infinity), independent of the Poisson process. This setting, in which the random field is independent of the point process, is often referred to as geostatistical marking. We examine how typical properties of interest in stochastic geometry and percolation theory, such as coverage probabilities and the existence of long-range connections, differ between Gilbert's model with radii given by some random field and Gilbert's model with radii assigned independently, but with the same marginal distribution. Among our main observations we find that complete coverage of R(2 )does not necessarily happen simultaneously, and that the spatial dependence induced by the random field may both increase as well as decrease the critical threshold for percolation.

  • 13.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    A homogeneity test of large dimensional covariance matrices under non-normality2018In: Kybernetika (Praha), ISSN 0023-5954, E-ISSN 1805-949X, Vol. 54, no 5, p. 908-920Article in journal (Refereed)
    Abstract [en]

    A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as U-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.

  • 14.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    A significance test of the RV coefficient in high dimensions2019In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 131, p. 116-130Article in journal (Refereed)
    Abstract [en]

    The RV coefficient is an important measure of linear dependence between two multivariate data vectors. Using unbiased and computationally efficient estimators of its components, a modification to the RV coefficient is proposed, and used to construct a test of significance for the true coefficient. The modified estimator improves the accuracy of the original and, along with the test, can be applied to data with arbitrarily large dimensions, possibly exceeding the sample size, and the underlying distribution need only have finite fourth moment. Exact and asymptotic properties are studied under fairly general conditions. The accuracy of the modified estimator and the test is shown through simulations under a variety of parameter settings. In comparisons against several existing methods, both the proposed estimator and the test exhibit similar performance to the distance correlation. Several real data applications are also provided.

  • 15.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    A unified approach to testing mean vectors with large dimensions2019In: AStA Advances in Statistical Analysis, ISSN 1863-8171, E-ISSN 1863-818X, Vol. 103, no 4, p. 593-618Article in journal (Refereed)
    Abstract [en]

    A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance matrices. Beginning with one-sample case, the construction of tests, underlying assumptions and asymptotic theory, is systematically extended to multi-sample case. Tests are defined in terms of U-statistics-based consistent estimators, and their limits are derived under a few mild assumptions. Accuracy of the tests is shown through simulations. Real data applications, including a five-sample unbalanced MANOVA analysis on count data, are also given.

  • 16.
    Ahmad, M Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Generalized tests of correlation for vectors with large dimensions using modified RV coefficient2019Report (Other academic)
    Abstract [en]

    Tests of zero correlation between two or more vectors with large dimension, possibly largerthan the sample size, are considered when the data may not necessarily follow a normal distribution. A single sample case for several vectors is rst proposed, which is then extended tothe common covariance matrix under the assumption of homogeneity across several independentpopulations. The test statistics are constructed using a recently proposed modicationof the RV coecient for high-dimensional vectors. The accuracy of the tests is shown through simulations.

  • 17.
    Ahmad, M Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Location-invariant and non-invariant tests for large dimensional covariance matrices under normality and non-normality2014Report (Other academic)
    Abstract [en]

    Test statistics for homogeneity, sphericity and identity of high-dimensional covariance matrices are presented under a wide variety of very general conditions when the dimension of the vector, $p$, may exceed the sample size, $n_i$, $i = 1, \ldots, g$. First, location-invariant tests are presented under normality assumption, followed by their robustness to normality by replacing the normality assumption with a mild alternative multivariate model. The two types of tests are then presented in non-invariant form, again under normality and non-normality. Tests of homogeneity of covariance matrices in all cases are immediately supplemented by the tests for sphericity and identity of the common covariance matrix under the null hypothesis. Both location-invariant and non-invariant tests are composed of estimators that are defined as $U$-statistics with kernels of different degrees. Hence, the asymptotic theory of $U$-statistics is employed to arrive at the limiting null and alternative distributions of tests for all cases. These limit distributions are derived using a very mild and practically viable set of assumptions mainly on the traces of the unknown covariance matrices. Finally, corrections and improvements of a few other tests are also presented.

  • 18.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension2017In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 44, no 2, p. 500-523Article in journal (Refereed)
    Abstract [en]

    For two or more multivariate distributions with common covariance matrix, test statistics for certain special structures of the common covariance matrix are presented when the dimension of the multivariate vectors may exceed the number of such vectors. The test statistics are constructed as functions of location-invariant estimators defined as U-statistics, and the corresponding asymptotic theory is used to derive the limiting distributions of the proposed tests. The properties of the test statistics are established under mild and practical assumptions, and the same are numerically demonstrated using simulation results with small or moderate sample sizes and large dimensions.

  • 19.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Location-invariant tests of homogeneity of large-dimensional covariance matrices2017In: Journal of Statistical Theory and Practice, ISSN 1559-8608, E-ISSN 1559-8616, Vol. 11, no 4, p. 731-745Article in journal (Refereed)
    Abstract [en]

    A test statistic for homogeneity of two or more covariance matrices of large dimensions is presented when the data are multivariate normal. The statistic is location-invariant and defined as a function of U-statistics of non-degenerate kernels so that the corresponding asymptotic theory is employed to derive the limiting normal distribution of the test under a few mild and practical assumptions. Accuracy of the test is shown through simulations with different parameter settings.

  • 20.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Multiple comparisons of mean vectors with large dimension under general conditions2019In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, no 6, p. 1044-1059Article in journal (Refereed)
    Abstract [en]

    Multiple comparisons for two or more mean vectors are considered when the dimension of the vectors may exceed the sample size, the design may be unbalanced, populations need not be normal, and the true covariance matrices may be unequal. Pairwise comparisons, including comparisons with a control, and their linear combinations are considered. Under fairly general conditions, the asymptotic multivariate distribution of the vector of test statistics is derived whose quantiles can be used in multiple testing. Simulations are used to show the accuracy of the tests. Real data applications are also demonstrated.

  • 21.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. Uppsala Univ, Dept Stat, Uppsala, Sweden.
    On Testing Sphericity and Identity of a Covariance Matrix with Large Dimensions2016In: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 25, no 2, p. 121-132Article in journal (Refereed)
    Abstract [en]

    Tests for certain covariance structures, including sphericity, are presented when the data may be high-dimensional but not necessarily normal. The tests are formulated as functions of location-invariant estimators defined as U-statistics of higher order kernels. Under a few mild assumptions, the limit distributions of the tests are shown to be normal. The accuracy of the tests is demonstrated by simulations.

  • 22.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality2017In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 8, p. 3738-3753Article in journal (Refereed)
    Abstract [en]

    A test for homogeneity of g 2 covariance matrices is presented when the dimension, p, may exceed the sample size, n(i), i = 1, ..., g, and the populations may not be normal. Under some mild assumptions on covariance matrices, the asymptotic distribution of the test is shown to be normal when n(i), p . Under the null hypothesis, the test is extended for common covariance matrix to be of a specified structure, including sphericity. Theory of U-statistics is employed in constructing the tests and deriving their limits. Simulations are used to show the accuracy of tests.

  • 23.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Tests for independence of vectors with large dimension2017Report (Other academic)
    Abstract [en]

    Given a random sample of n iid vectors, each of dimension p and partitioned into b sub- vectors of sizes pi, i = 1;:::;b. Location-invariant and non-invariant test statistics for independence of sub-vectors are presented when pi may exceed n and the distribution need not be normal. The tests are composed of U -statistics based estimators of the Frobenius norm of the di erence between the null and alternative hypotheses. Asymptotic distributions of the tests are provided for n;pi! 1, where their nite-sample performance is demonstrated through simulations. Some related and subsequent tests are brie y described. Relations of the proposed tests to certain multivariate measures are discussed, which are of interest on their own.

  • 24.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Tests of Zero Correlation Using Modified RV Coefficient for High-Dimensional Vectors2019In: Journal of Statistical Theory and Practice, ISSN 1559-8608, E-ISSN 1559-8616, Vol. 13, no 3, article id 43Article in journal (Refereed)
    Abstract [en]

    Tests of zero correlation between two or more vectors with large dimension, possibly larger than the sample size, are considered when the data may not necessarily follow a normal distribution. A single-sample case for several vectors is first proposed, which is then extended to the common covariance matrix under the assumption of homogeneity across several independent populations. The test statistics are constructed using a recently proposed modification of the RV coefficient (a correlation coefficient for vector-valued random variables) for high-dimensional vectors. The accuracy of the tests is shown through simulations.

  • 25.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Pavlenko, Tatjana
    KTH, Stockholm, Sweden.
    A U-classifier for high-dimensional data under non-normality2018In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 167, p. 269-283Article in journal (Refereed)
    Abstract [en]

    A classifier for two or more samples is proposed when the data are high-dimensional and the distributions may be non-normal. The classifier is constructed as a linear combination of two easily computable and interpretable components, the U-component and the P-component. The U-component is a linear combination of U-statistics of bilinear forms of pairwise distinct vectors from independent samples. The P-component, the discriminant score, is a function of the projection of the U-component on the observation to be classified. Together, the two components constitute an inherently bias-adjusted classifier valid for high-dimensional data. The classifier is linear but its linearity does not rest on the assumption of homoscedasticity. Properties of the classifier and its normal limit are given under mild conditions. Misclassification errors and asymptotic properties of their empirical counterparts are discussed. Simulation results are used to show the accuracy of the proposed classifier for small or moderate sample sizes and large dimensions. Applications involving real data sets are also included.

  • 26.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    von Rosen, D.
    Tests for high-dimensional covariance matrices using the theory of U-statistics2015In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 85, no 13, p. 2619-2631Article in journal (Refereed)
    Abstract [en]

    Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.

  • 27.
    Ahmad, M. Rauf
    et al.
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Von Rosen, Dietrich
    Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality2015In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 44, no 7, p. 1387-1398Article in journal (Refereed)
    Abstract [en]

    Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp >> n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.

  • 28.
    Ahmady Phoulady, Hady
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Brownian Motions and Scaling Limits of Random Trees2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
  • 29.
    Albert, Michael
    et al.
    Univ Otago, Dept Comp Sci, Dunedin, New Zealand.
    Holmgren, Cecilia
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Johansson, Tony
    Stockholm Univ, Dept Math, Stockholm, Sweden.
    Skerman, Fiona
    Masaryk Univ, Fac Informat, Brno, Czech Republic.
    Embedding Small Digraphs and Permutations in Binary Trees and Split Trees2020In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 82, no 3, p. 589-615Article in journal (Refereed)
    Abstract [en]

    We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees (Cai et al. in Combin Probab Comput 28(3):335-364, 2019). We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye (SIAM J Comput 28(2):409-432, 1998. 10.1137/s0097539795283954). Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree, with probability tending to one as the number of balls increases, the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embeddings of digraphs into split trees which may be of independent interest.

  • 30.
    Ali, Mohammad
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
    Performance of Three Classification Techniques in Classifying Credit Applications Into Good Loans and Bad Loans: A Comparison2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The use of statistical classification techniques in classifying loan applications into good loans and bad loans gained importance with the exponential increase in the demand for credit. It is paramount to use a classification technique with a high predictive capacity to ensure the profitability of the business venture.

     

    In this study we aim to compare the predictive capability of three classification techniques: 1) Logistic regression, 2) CART, and 3) random forests. We apply these techniques on German credit data using an 80:20 learning:test split, and compare the performance of the models fitted using the three classification techniques. The probability of default pi for each observation in the test set is calculated using the models fitted on the training dataset. Each test set sample xi is then classified into a good loan or a bad loan, based on a threshold , such that xi bad loan class if pi  . We chose several  thresholds in order to compare the performance of each of the three classification techniques on five model suitability statistics: Accuracy, precision, negative predictive value, recall, and specificity.

     

    None of the classifiers turned out to be best at all the five cross-validation statistics. However, logistic regression has the best performance at low probability of default thresholds. On the other hand, for higher thresholds, CART performs best in accuracy, precision, and specificity measures, while random forest performs best for negative predictive value and recall measures. 

  • 31.
    Allander, Erik
    et al.
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Bring, Johan
    Gudmundsson, Ludvig
    Mattson, Stefan
    Olafsson, Olafur
    Rigner, Karl-Gustav
    Sigurgeirsson, Bardur
    Taube, Adam
    What is the long term value of multiphasic screening and the initial judgement of benefit?1997In: Scandinavian Journal of Social Medicine, Vol. Suppl 51, p. 1-20Article in journal (Refereed)
  • 32.
    Alm, Sven Erick
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
    Approximation and Simulation of the Distributions of Scan Statistics for Poisson Processes in Higher Dimensions1998In: Extremes, Vol. 1, p. 111-126Article in journal (Refereed)
    Abstract [en]

    Given a Poisson process in two or three dimensions we are interested in the scan statistic, i.e. the largest number of points contained in a translate of a fixed scanning set restricted to lie inside a rectangular area.

    The distribution of the scan statistic is accurately approximated for rectangular scanning sets, using a technique that is also extended to higher dimensions.

    The accuracy of the approximation is checked through simulation.

  • 33.
    Alm, Sven Erick
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
    Monotonicity of the difference between median and mean of gamma distributions and of a related Ramanujan sequence2003In: Bernoulli, ISSN 1350-7265, Vol. 9, no 2, p. 351-371Article in journal (Refereed)
    Abstract [en]

    For $n\ge0$, let $\lambda_n$ be the median of the $\Gamma(n+1,1)$ distribution. We prove that the sequence $\{\alpha_n=\lambda_n-n\}$ decreases from $\log 2$ to $2/3$ as $n$ increases from 0 to $\infty$. The difference, $1-\alpha_n$, between the mean and the median thus increases from $1-\log 2$ to $1/3$.

    This result also proves the following conjecture by Chen \& Rubin about the Poisson distributions: Let $Y_{\mu}\sim\text{Poisson}(\mu)$, and \lambda_n$ be the largest $\mu$ such that $P(Y_{\mu}\le n)=1/2$, then $\lambda_n-n$ is decreasing in $n$.

    The sequence $\{\alpha_n\}$ is related to a sequence $\{\theta_n\}$, introduced by Ramanujan, which is known to be decreasing and of the form

    $\theta_n=\frac13+\frac4{135(n+k_n)}$, where $\frac2{21}<k_n\le\frac8{45}$. We also show that the sequence $\{k_n\}$ is decreasing.

  • 34.
    Alm, Sven Erick
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    On Measures of Average Degree for Lattices2006In: Combinatorics, Probability and Computing, Vol. 15, no 4, p. 477-488Article in journal (Refereed)
    Abstract [en]

    The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices.

    These measures are compared on a class of lattices and are analyzed using a Markov chain describing a random walk on the lattice. Using the new measure, we conjecture the order of both the critical probabilities for bond percolation and the connective constants for self-avoiding walks on these lattices.

  • 35.
    Alm, Sven Erick
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
    Deijfen, Maria
    Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden..
    First Passage Percolation on \(\mathbb {Z}^2\): A Simulation Study2015In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, no 3, p. 657-678Article in journal (Refereed)
    Abstract [en]

    First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.

  • 36.
    Alm, Sven Erick
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Janson, Svante
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Linusson, Svante
    First critical probability for a problem on random orientations in G(n,p)2014In: Electronic Journal of Probability, ISSN 1083-6489, E-ISSN 1083-6489, Vol. 19, p. 69-Article in journal (Refereed)
    Abstract [en]

    We study the random graph G (n,p) with a random orientation. For three fixed vertices s, a, b in G(n,p) we study the correlation of the events {a -> s} (there exists a directed path from a to s) and {s -> b}. We prove that asymptotically the correlation is negative for small p, p < C-1/n, where C-1 approximate to 0.3617, positive for C-1/n < p < 2/n and up to p = p(2)(n). Computer aided computations suggest that p(2)(n) = C-2/n, with C-2 approximate to 7.5. We conjecture that the correlation then stays negative for p up to the previously known zero at 1/2; for larger p it is positive.

  • 37.
    Alm, Sven Erick
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
    Parviainen, Robert
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics. Matematisk statistik.
    Bounds for the connective constant of the hexagonal lattice2004In: J.\ Phys. A: Math. Gen., Vol. 37, p. 549-Article in journal (Refereed)
    Abstract [en]

    We give improved bounds for the connective constant of the hexagonal lattice. The lower bound is found by using Kesten's method of irreducible bridges and by determining generating functions for bridges on one-dimensional lattices.

    The upper bound is obtained as the largest eigenvalue of a certain transfer matrix. Using a relation between the hexagonal and the $(3.12^2)$ lattices, we also give bounds for the connective constant of the latter lattice.

  • 38.
    Alm, Sven Erick
    et al.
    Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
    Parviainen, Robert
    Lower and Upper Bounds for the Time Constant of First-Passage Percolation2001Report (Other scientific)
  • 39.
    Almesjö, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    Regression modeling of cyclotron spare parts consumption2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
  • 40.
    Aly, S. M.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    From Moment Explosion To The Asymptotic Behavior Of The Cumulative Distribution For A Random Variable2017In: Theory of Probability and its Applications, ISSN 0040-585X, E-ISSN 1095-7219, Vol. 61, no 3, p. 357-374Article in journal (Refereed)
    Abstract [en]

    We study the Tauberian relations between the moment generating function (MGF) and the complementary cumulative distribution function of a random variable whose MGF is finite only on part of the real line. We relate the right tail behavior of the cumulative distribution function of such a random variable to the behavior of its MGF near the critical moment. We apply our results to an arbitrary superposition of a CIR process and the time-integral of this process.

  • 41. Amiri, Saeid
    A comparison of bootstrap methods for variance estimation2010In: Journal of Statistical Theory and ApplicationsArticle in journal (Refereed)
    Abstract [en]

    This paper presents a comparison of the nonparametric and parametric bootstrapmethods, when the statistic of interest is the sample variance estimator. Conditionswhen the nonparametric bootstrap method of variance performs better than the para-metric bootstrap method are described

  • 42. Amiri, Saeid
    On Resampling for the Contingency Table based on Information EnergyManuscript (preprint) (Other academic)
    Abstract [en]

    The bootstrap method is studied herein for the analysis of categorical data,in particular for the contin­gency table. The way to carry out atest of association is to bootstrap on the basis of expected values that havealready been ascertained by a few authors. This paper shows the theoreticalapproach of bootstrapping for a contingency table, and the idea which it isbased on has been inspired by the use of the informational energy func­tion.The properties of the proposed tests are illustrated and discussed using MonteCarlo simulations. The paper ends with analytical examples that elucidate the use ofthe proposed tests.

  • 43.
    Amiri, Saeid
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On the Application of the Bootstrap: Coefficient of Variation, Contingency Table, Information Theory and Ranked Set Sampling2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis deals with the bootstrap method. Three decades after the seminal paper by Bradly Efron, still the horizons of this method need more exploration. The research presented herein has stepped into different fields of statistics where the bootstrap method can be utilized as a fundamental statistical tool in almost any application. The thesis considers various statistical problems, which is explained briefly below.

    Bootstrap method: A comparison of the parametric and the nonparametric bootstrap of variance is presented. The bootstrap of ranked set sampling is dealt with, as well as the wealth of theories and applications on the RSS bootstrap that exist nowadays. Moreover, the performance of RSS in resampling is explored. Furthermore, the application of the bootstrap method in the inference of contingency table test is studied.

    Coefficient of variation: This part shows the capacity of the bootstrap for inferring the coefficient of variation, a task which the asymptotic method does not perform very well.

    Information theory: There are few works on the study of information theory, especially on the inference of entropy. The papers included in this thesis try to achieve the inference of entropy using the bootstrap method. 

    List of papers
    1. A comparison of bootstrap methods for variance estimation
    Open this publication in new window or tab >>A comparison of bootstrap methods for variance estimation
    2010 (English)In: Journal of Statistical Theory and ApplicationsArticle in journal (Refereed) Published
    Abstract [en]

    This paper presents a comparison of the nonparametric and parametric bootstrapmethods, when the statistic of interest is the sample variance estimator. Conditionswhen the nonparametric bootstrap method of variance performs better than the para-metric bootstrap method are described

    Keywords
    Bootstrap; Nonparametric; Parametric; Kurtosis; Variance.
    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:uu:diva-158976 (URN)
    Available from: 2011-09-19 Created: 2011-09-19
    2. On the Resampling of the Unbalanced Ranked Set Sample
    Open this publication in new window or tab >>On the Resampling of the Unbalanced Ranked Set Sample
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    This paper considers the bootstrap approach of the unbalanced Ranked Set Sampling (RSS) method. Herethe sequence bootstrap is used to shift the analysis of the unbalanced RSS method to an analysis ofthe balanced RSS sample, and balanced RSS is also discussed. Here the consequences of differentalgorithms for carrying out resampling are discussed. The pro­posed methods are studied using Monte Carloinvestigations. Furthermore, the theoretical approach is discussed.

    Keywords
    Bootstrap method; Monte Carlo simulation; Ranked set sample
    National Category
    Probability Theory and Statistics
    Research subject
    Statistics
    Identifiers
    urn:nbn:se:uu:diva-158983 (URN)
    Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2012-02-16
    3. On the efficiency of bootstrap method into the analysis contingency table
    Open this publication in new window or tab >>On the efficiency of bootstrap method into the analysis contingency table
    2011 (English)In: Computer Methods and Programs in Biomedicine, ISSN 0169-2607, E-ISSN 1872-7565, Vol. 104, no 2, p. 182-187Article in journal (Refereed) Published
    Abstract [en]

    The bootstrap method is a computer intensive statistical method that is widely used in performing nonparametric inference. Categorica ldata analysis,inparticular the analysis of contingency tables, is commonly used in applied field. This work considers nonparametric bootstrap tests for the analysis of contingency tables. There are only a few research papers which exploit this field. The p-values of tests in contingency tables are discrete and should be uniformly distributed under the null hypothesis. The results of this article show that corresponding bootstrap versions work better than the standard tests. Properties of the proposed tests are illustrated and discussed using Monte Carlo simulations. This article concludes with an analytical example that examines the performance of the proposed tests and the confidence interval of the association coefficient.

    Keywords
    Association coefficient, Bootstrap method, Chi-squared test, Contingency table, Monte Carlo simulation
    National Category
    Probability Theory and Statistics
    Identifiers
    urn:nbn:se:uu:diva-158978 (URN)10.1016/j.cmpb.2011.01.007 (DOI)000296945100018 ()
    Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2017-12-08Bibliographically approved
    4. An Improvement of the Nonparametric Bootstrap Test for the Comparison of the Coefficient of Variations
    Open this publication in new window or tab >>An Improvement of the Nonparametric Bootstrap Test for the Comparison of the Coefficient of Variations
    2010 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 39, no 9, p. 1726-1734Article in journal (Refereed) Published
    Abstract [en]

    In this article, we propose a new test for examining the equality of the coefficient of variation between two different populations. The proposed test is based on the nonparametric bootstrap method. It appears to yield several appreciable advantages over the current tests. The quick and easy implementation of the test can be considered as advantages of the proposed test. The test is examined by the Monte Carlo simulations, and also evaluated using various numerical studies.

    Keywords
    Bootstrap method, Coefficient of variation, Monte Carlo simulation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:uu:diva-134888 (URN)10.1080/03610918.2010.512693 (DOI)000282124000004 ()
    Available from: 2010-12-02 Created: 2010-12-02 Last updated: 2017-12-12Bibliographically approved
    5. Assessing the coefficient of variations of chemical data using bootstrap method
    Open this publication in new window or tab >>Assessing the coefficient of variations of chemical data using bootstrap method
    2011 (English)In: Journal of Chemometrics, ISSN 0886-9383, E-ISSN 1099-128X, Vol. 25, no 6, p. 295-300Article in journal (Refereed) Published
    Abstract [en]

    The coefficient of variation is frequently used in the comparison and precision of results with different scales. This work examines the comparison of the coefficient of variation without any assumptions about the underlying distribution. A family of tests based on the bootstrap method is proposed, and its properties are illustrated using Monte Carlo simulations. The proposed method is applied to chemical experiments with iid and non-iid observations.

    Keywords
    bootstrap method, coefficient of variation, Monte Carlo simulation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:uu:diva-156490 (URN)10.1002/cem.1350 (DOI)000292542300002 ()
    Available from: 2011-07-25 Created: 2011-07-25 Last updated: 2017-12-08Bibliographically approved
    6. The Comparison of Entropies  using the Resampling Method
    Open this publication in new window or tab >>The Comparison of Entropies  using the Resampling Method
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    This paper discusses the bootstrap test of entropies. Since the comparison of entropies is of prime interestin applied fields, finding an appropriate way to carry out such a comparison is of the utmost importance. This paperpresents how resampling should be performed to obtain an accurate p-value. Although the test using a pair-wise bootstrapconfidence interval has already been dealt with in some works, here the bootstrap tests are studied because it may demand quite adifferent resampling algorithm compared with the confidence interval. Moreover, the multiple test is studied. The proposed testsappear to yield several appreciable advantages. The easy implementation and the power of the proposed test can be considered asadvantages. Here the entropy of discrete and continuous variables is studied. The proposed tests are examined using Monte Carloinvestigations, and also evaluated using various distributions.

    Keywords
    Bootstrap method; Entropy; Jackknife; Monte Carlo investigation; Multiple test
    National Category
    Probability Theory and Statistics
    Research subject
    Statistics
    Identifiers
    urn:nbn:se:uu:diva-159210 (URN)
    Available from: 2011-09-25 Created: 2011-09-25 Last updated: 2012-02-16
    7. On Resampling for the Contingency Table based on Information Energy
    Open this publication in new window or tab >>On Resampling for the Contingency Table based on Information Energy
    (English)Manuscript (preprint) (Other academic)
    Abstract [en]

    The bootstrap method is studied herein for the analysis of categorical data,in particular for the contin­gency table. The way to carry out atest of association is to bootstrap on the basis of expected values that havealready been ascertained by a few authors. This paper shows the theoreticalapproach of bootstrapping for a contingency table, and the idea which it isbased on has been inspired by the use of the informational energy func­tion.The properties of the proposed tests are illustrated and discussed using MonteCarlo simulations. The paper ends with analytical examples that elucidate the use ofthe proposed tests.

    Keywords
    Bootstrap method; Chi-squared test; Contingency table; Informational energy; Monte Carlo investigation
    National Category
    Probability Theory and Statistics
    Research subject
    Statistics
    Identifiers
    urn:nbn:se:uu:diva-158980 (URN)
    Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2011-09-25
  • 44.
    Amiri, Saeid
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    On the Resampling of the Unbalanced Ranked Set SampleManuscript (preprint) (Other academic)
    Abstract [en]

    This paper considers the bootstrap approach of the unbalanced Ranked Set Sampling (RSS) method. Herethe sequence bootstrap is used to shift the analysis of the unbalanced RSS method to an analysis ofthe balanced RSS sample, and balanced RSS is also discussed. Here the consequences of differentalgorithms for carrying out resampling are discussed. The pro­posed methods are studied using Monte Carloinvestigations. Furthermore, the theoretical approach is discussed.

  • 45.
    Amiri, Saeid
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    The Comparison of Entropies  using the Resampling MethodManuscript (preprint) (Other academic)
    Abstract [en]

    This paper discusses the bootstrap test of entropies. Since the comparison of entropies is of prime interestin applied fields, finding an appropriate way to carry out such a comparison is of the utmost importance. This paperpresents how resampling should be performed to obtain an accurate p-value. Although the test using a pair-wise bootstrapconfidence interval has already been dealt with in some works, here the bootstrap tests are studied because it may demand quite adifferent resampling algorithm compared with the confidence interval. Moreover, the multiple test is studied. The proposed testsappear to yield several appreciable advantages. The easy implementation and the power of the proposed test can be considered asadvantages. Here the entropy of discrete and continuous variables is studied. The proposed tests are examined using Monte Carloinvestigations, and also evaluated using various distributions.

  • 46.
    Amiri, Saeid
    et al.
    Univ Wisconsin, Dept Nat & Appl Sci, Green Bay, WI 54302 USA..
    Modarres, Reza
    George Washington Univ, Dept Stat, Washington, DC 20052 USA..
    Zwanzig, Silvelyn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    Tests of perfect judgment ranking using pseudo-samples2017In: Computational statistics (Zeitschrift), ISSN 0943-4062, E-ISSN 1613-9658, Vol. 32, no 4, p. 1309-1322Article in journal (Refereed)
    Abstract [en]

    Ranked set sampling (RSS) is a sampling approach that can produce improved statistical inference when the ranking process is perfect. While some inferential RSS methods are robust to imperfect rankings, other methods may fail entirely or provide less efficiency. We develop a nonparametric procedure to assess whether the rankings of a given RSS are perfect. We generate pseudo-samples with a known ranking and use them to compare with the ranking of the given RSS sample. This is a general approach that can accommodate any type of raking, including perfect ranking. To generate pseudo-samples, we consider the given sample as the population and generate a perfect RSS. The test statistics can easily be implemented for balanced and unbalanced RSS. The proposed tests are compared using Monte Carlo simulation under different distributions and applied to a real data set.

  • 47.
    Amiri, Saeid
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    von Rosen, Dietrich
    On the efficiency of bootstrap method into the analysis contingency table2011In: Computer Methods and Programs in Biomedicine, ISSN 0169-2607, E-ISSN 1872-7565, Vol. 104, no 2, p. 182-187Article in journal (Refereed)
    Abstract [en]

    The bootstrap method is a computer intensive statistical method that is widely used in performing nonparametric inference. Categorica ldata analysis,inparticular the analysis of contingency tables, is commonly used in applied field. This work considers nonparametric bootstrap tests for the analysis of contingency tables. There are only a few research papers which exploit this field. The p-values of tests in contingency tables are discrete and should be uniformly distributed under the null hypothesis. The results of this article show that corresponding bootstrap versions work better than the standard tests. Properties of the proposed tests are illustrated and discussed using Monte Carlo simulations. This article concludes with an analytical example that examines the performance of the proposed tests and the confidence interval of the association coefficient.

  • 48. Amiri, Saeid
    et al.
    von Rosen, Dietrich
    Zwanzig, Silvelyn
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
    The SVM Approach for Box–Jenkins Models 2009In: REVSTAT-Statistical Journal, ISSN 1645-6726, Vol. 7, no 1, p. 23-36Article in journal (Refereed)
    Abstract [en]

    Support Vector Machine (SVM) is known in classification and regression modeling. It has been receiving attention in the application of nonlinear functions. The aim is to motivate the use of the SVM approach to analyze the time series models. This is an effort to assess the performance of SVM in comparison with ARMA model. The applicability of this approach for a unit root situation is also considered.

  • 49.
    Amiri, Saied
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On the Application of the Transformation to Testing the Coeffcient of VariationManuscript (preprint) (Other academic)
    Abstract [en]

    It is difficult to drive mathematically the theoretical sampling distribution of the coefficientof varia­tion (CV) and to make inferences about it. This paper attempts to provide an overview ofa parametric asymp­totic inference of the coefficient of variation using a transformation that gives variancestabilization. Although it can easily be shown that the variance of the logarithm of the sample mean is approximatelythe coeffi­cient of variation, up to now it has not been demonstrated how this idea can be used to draw inferences concerningthe CV. This article shows how the bootstrap method can be used to improve the discussed methods and deals with one- andtwo-sample tests of the CV.

  • 50.
    Anders Lindfors, Roland Roberts, Anders Christoffersson and Gunnar Anderlind
    Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
    Model based frequency domain estimation of the thermal properties of building insulation1995In: J. Thermal Insul. and bldg. envs., Vol. 18, no 1, p. 31-Article in journal (Refereed)
1234567 1 - 50 of 1041
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