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• 1.
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.
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.
Re: Long-term survival and mortality in prostate cancer treated with noncurative intent1995In: UROLGY, Vol. 154, p. 460-465Article in journal (Refereed)
• 3.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
25 years of applied statistics1998In: JOURNAL OF APPLIED STATISTICS, ISSN 0266-4763, Vol. 25, no 1, p. 3-22Article in journal (Refereed)
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
Risk for endometrial cancer following breast cancer: A prospective study in Sweden1997In: Cancer Causes & Control, Vol. 8, p. 821-827Article in journal (Refereed)
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
A prospective study of smoking and risk of prostate cancer1996In: Int J Cancer, Vol. 67, p. 764-768Article in journal (Refereed)
• 6.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
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.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
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

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.
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)

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.

• 9.
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)

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.

• 10.
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)

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.

• 11.
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)

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.

• 12.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
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)

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.

• 13.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
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)

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.

• 14.
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
• 15.
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

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$\in$ bad loan class if pi  $\alpha$. We chose several $\alpha$ 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.

• 16.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
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)
• 17.
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)

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.

• 18.
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)

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. • 19. 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) 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. • 20. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. 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) 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. • 21. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. 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) 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. • 22. 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. 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) 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.

• 23.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
Lower and Upper Bounds for the Time Constant of First-Passage Percolation2001Report (Other scientific)
• 24.
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
• 25.
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)

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.

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

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

• 27. Amiri, Saeid
On Resampling for the Contingency Table based on Information EnergyManuscript (preprint) (Other academic)

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.

• 28.
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)

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.

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

##### Keyword
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
##### 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.

##### Keyword
Bootstrap method; Monte Carlo simulation; Ranked set sample
##### National Category
Probability Theory and Statistics
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.

##### Keyword
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.

##### Keyword
Bootstrap method, Coefficient of variation, Monte Carlo simulation
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.

##### Keyword
bootstrap method, coefficient of variation, Monte Carlo simulation
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
##### 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.

##### Keyword
Bootstrap method; Entropy; Jackknife; Monte Carlo investigation; Multiple test
##### National Category
Probability Theory and Statistics
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
##### 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.

##### Keyword
Bootstrap method; Chi-squared test; Contingency table; Informational energy; Monte Carlo investigation
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-158980 (URN)
Available from: 2011-09-19 Created: 2011-09-19 Last updated: 2011-09-25
• 29.
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)

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.

• 30.
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)

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.

• 31.
Univ Wisconsin, Dept Nat & Appl Sci, Green Bay, WI 54302 USA..
George Washington Univ, Dept Stat, Washington, DC 20052 USA.. 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)

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.

• 32.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
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)

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.

• 33. Amiri, Saeid
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)

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.

• 34.
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)

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.

• 35.
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)
• 36.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
An Evaluation of Hypothesis Testing Methods for Equating Differences in Kernel EquatingManuscript (preprint) (Other academic)

In observed-score equating, hypothesis tests of equating differences are helpful in deciding which equating function is suitable. Here, a hypothesis testing procedure for item response theory (IRT) observed-score kernel equating using a Wald test is introduced. Simulations evaluating the Wald test when using IRT and log-linear models are conducted. The test with either IRT or log-linear models is shown to have high power and greatly outperform the Hommel multiple hypothesis testing method. The Wald test is applied to two datasets in both an equivalent groups design and a non-equivalent groups design, showing that the Wald test can provide different conclusions to other hypothesis testing methods in practice.

• 37.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Contributions to Kernel Equating2014Doctoral thesis, comprehensive summary (Other academic)

The statistical practice of equating is needed when scores on different versions of the same standardized test are to be compared. This thesis constitutes four contributions to the observed-score equating framework kernel equating.

Paper I introduces the open source R package kequate which enables the equating of observed scores using the kernel method of test equating in all common equating designs. The package is designed for ease of use and integrates well with other packages. The equating methods non-equivalent groups with covariates and item response theory observed-score kernel equating are currently not available in any other software package.

In paper II an alternative bandwidth selection method for the kernel method of test equating is proposed. The new method is designed for usage with non-smooth data such as when using the observed data directly, without pre-smoothing. In previously used bandwidth selection methods, the variability from the bandwidth selection was disregarded when calculating the asymptotic standard errors. Here, the bandwidth selection is accounted for and updated asymptotic standard error derivations are provided.

Item response theory observed-score kernel equating for the non-equivalent groups with anchor test design is introduced in paper III. Multivariate observed-score kernel equating functions are defined and their asymptotic covariance matrices are derived. An empirical example in the form of a standardized achievement test is used and the item response theory methods are compared to previously used log-linear methods.

In paper IV, Wald tests for equating differences in item response theory observed-score kernel equating are conducted using the results from paper III. Simulations are performed to evaluate the empirical significance level and power under different settings, showing that the Wald test is more powerful than the Hommel multiple hypothesis testing method. Data from a psychometric licensure test and a standardized achievement test are used to exemplify the hypothesis testing procedure. The results show that using the Wald test can provide different conclusions to using the Hommel procedure.

1. Performing the Kernel Method of Test Equating with the Package kequate
Open this publication in new window or tab >>Performing the Kernel Method of Test Equating with the Package kequate
2013 (English)In: Journal of Statistical Software, ISSN 1548-7660, E-ISSN 1548-7660, Vol. 55, no 6, p. 1-25Article in journal (Refereed) Published
##### Abstract [en]

In standardized testing it is important to equate tests in order to ensure that the test takers, regardless of the test version given, obtain a fair test. Recently, the kernel method of test equating, which is a conjoint framework of test equating, has gained popularity. The kernel method of test equating includes five steps: (1) pre-smoothing, (2) estimation of the score probabilities, (3) continuization, (4) equating, and (5) computing the standard error of equating and the standard error of equating difference. Here, an implementation has been made for six different equating designs: equivalent groups, single group, counterbalanced, non-equivalent groups with anchor test using either chain equating or post-stratification equating, and non-equivalent groups using covariates. An R package for the kernel method of test equating called kequate is presented. Included in the package are also diagnostic tools aiding in the search for a proper log-linear model in the pre-smoothing step for use in conjunction with the R function glm.

##### Place, publisher, year, edition, pages
American Statistical Association, 2013
##### Keyword
observed-score test equating, R package, kernel equating, item-response theory
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-208912 (URN)000325948000001 ()
Available from: 2013-10-23 Created: 2013-10-10 Last updated: 2017-12-06Bibliographically approved
2. Improving the Bandwidth Selection in Kernel Equating
Open this publication in new window or tab >>Improving the Bandwidth Selection in Kernel Equating
2014 (English)In: Journal of educational measurement, ISSN 0022-0655, E-ISSN 1745-3984, Vol. 51, no 3, p. 223-238Article in journal (Refereed) Published
##### Abstract [en]

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners for being too complex and that it does not offer sufficient smoothing in certain cases. In addition, the bandwidth parameters have been treated as constants in the derivation of the standard error of equating even when they were selected by considering the observed data. Here, the bandwidth selection is simplified, and modified standard errors of equating (SEEs) that reflect the bandwidth selection method are derived. The method is illustrated with real data examples and simulated data.

##### Place, publisher, year, edition, pages
Blackwell Publishing, 2014
##### Keyword
kernel equating, observed-score test equating
##### National Category
Probability Theory and Statistics
Statistics
##### Identifiers
urn:nbn:se:uu:diva-223988 (URN)10.1111/jedm.12044 (DOI)000341592200001 ()
Available from: 2014-04-29 Created: 2014-04-29 Last updated: 2017-12-05Bibliographically approved
3. Item Response Theory Observed-Score Kernel Equating
Open this publication in new window or tab >>Item Response Theory Observed-Score Kernel Equating
2017 (English)In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 82, no 1, p. 46-66Article in journal (Refereed) Published
##### Abstract [en]

Item response theory (IRT) observed-score kernel equating is introduced for the non-equivalent groups with anchor test equating design using either chain equating or post-stratification equating. The equating function is treated in a multivariate setting and the asymptotic covariance matrices of IRT observed-score kernel equating functions are derived. Equating is conducted using the two-parameter and three-parameter logistic models with simulated data and data from a standardized achievement test. The results show that IRT observed-score kernel equating offers small standard errors and low equating bias under most settings considered.

##### Keyword
observed-score equating, item response theory, equipercentile equating, standard errors, NEAT design
##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:uu:diva-233484 (URN)10.1007/s11336-016-9528-7 (DOI)000394985400003 ()27743280 (PubMedID)
##### Funder
Swedish Research Council, 2014-578 Available from: 2014-10-21 Created: 2014-10-06 Last updated: 2017-04-20Bibliographically approved
4. An Evaluation of Hypothesis Testing Methods for Equating Differences in Kernel Equating
Open this publication in new window or tab >>An Evaluation of Hypothesis Testing Methods for Equating Differences in Kernel Equating
##### Abstract [en]

In observed-score equating, hypothesis tests of equating differences are helpful in deciding which equating function is suitable. Here, a hypothesis testing procedure for item response theory (IRT) observed-score kernel equating using a Wald test is introduced. Simulations evaluating the Wald test when using IRT and log-linear models are conducted. The test with either IRT or log-linear models is shown to have high power and greatly outperform the Hommel multiple hypothesis testing method. The Wald test is applied to two datasets in both an equivalent groups design and a non-equivalent groups design, showing that the Wald test can provide different conclusions to other hypothesis testing methods in practice.

##### National Category
Probability Theory and Statistics
##### Identifiers
urn:nbn:se:uu:diva-233486 (URN)
Available from: 2014-10-21 Created: 2014-10-06 Last updated: 2015-02-03
• 38.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Department of Statistics, USBE, Umeå University. Department of Statistics, USBE, Umeå University.
Performing the Kernel Method of Test Equating with the Package kequate2013In: Journal of Statistical Software, ISSN 1548-7660, E-ISSN 1548-7660, Vol. 55, no 6, p. 1-25Article in journal (Refereed)

In standardized testing it is important to equate tests in order to ensure that the test takers, regardless of the test version given, obtain a fair test. Recently, the kernel method of test equating, which is a conjoint framework of test equating, has gained popularity. The kernel method of test equating includes five steps: (1) pre-smoothing, (2) estimation of the score probabilities, (3) continuization, (4) equating, and (5) computing the standard error of equating and the standard error of equating difference. Here, an implementation has been made for six different equating designs: equivalent groups, single group, counterbalanced, non-equivalent groups with anchor test using either chain equating or post-stratification equating, and non-equivalent groups using covariates. An R package for the kernel method of test equating called kequate is presented. Included in the package are also diagnostic tools aiding in the search for a proper log-linear model in the pre-smoothing step for use in conjunction with the R function glm.

• 39.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Educational Testing Service.
Book review of M. J. Kolen & R. L. Brennan (2014) Test Equating, Scaling, and Linking: Methods and Practices Third Edition.2015In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 80, no 3, p. 856-858Article, book review (Other academic)
• 40.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Educational Testing Service.
Improving the Bandwidth Selection in Kernel Equating2014In: Journal of educational measurement, ISSN 0022-0655, E-ISSN 1745-3984, Vol. 51, no 3, p. 223-238Article in journal (Refereed)

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners for being too complex and that it does not offer sufficient smoothing in certain cases. In addition, the bandwidth parameters have been treated as constants in the derivation of the standard error of equating even when they were selected by considering the observed data. Here, the bandwidth selection is simplified, and modified standard errors of equating (SEEs) that reflect the bandwidth selection method are derived. The method is illustrated with real data examples and simulated data.

• 41.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Sensitivity analysis of violations of the faithfulness assumption2014In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 84, no 7, p. 1608-1620Article in journal (Refereed)

We study the implication of violations of the faithfulness condition due to parameter cancellations on estimation of the directed acyclic graph (DAG) skeleton. Three settings are investigated: when (i) faithfulness is guaranteed (ii) faithfulness is not guaranteed and (iii) the parameter distributions are concentrated around unfaithfulness (near-unfaithfulness). In a simulation study, the effects of the different settings are compared using the parents and children (PC) and max–min parents and children (MMPC) algorithms. The results show that the performance in the faithful case is almost unchanged compared with the unrestricted case, whereas there is a general decrease in performance under the near-unfaithful case as compared with the unrestricted case. The response to near-unfaithful parameterizations is similar between the two algorithms, with the MMPC algorithm having higher true positive rates and the PC algorithm having lower false positive rates.

• 42.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Umeå University.
IRT Observed-score Kernel Equating2014Report (Other academic)

Item response theory (IRT) observed-score kernel equating is described for thenon-equivalent groups with anchor test equating design using either chain equating orpost-stratification equating. The equating function is treated in a multivariate setting andthe asymptotic covariance matrices of IRT observed-score kernel equating functions arederived. Equating is conducted using the two-parameter and three-parameter logisticmodels with simulated data and data from a standardized achievement test. The resultsshow that IRT observed-score kernel equating offers small standard errors and low equatingbias under most settings considered.

• 43.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. Beijing Normal Univ, Beijing, Peoples R China..
Department of Statistics, USBE, Umeå University, Sweden..
Item Response Theory Observed-Score Kernel Equating2017In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 82, no 1, p. 46-66Article in journal (Refereed)

Item response theory (IRT) observed-score kernel equating is introduced for the non-equivalent groups with anchor test equating design using either chain equating or post-stratification equating. The equating function is treated in a multivariate setting and the asymptotic covariance matrices of IRT observed-score kernel equating functions are derived. Equating is conducted using the two-parameter and three-parameter logistic models with simulated data and data from a standardized achievement test. The results show that IRT observed-score kernel equating offers small standard errors and low equating bias under most settings considered.

• 44.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences.
On the use of two-phase sampling in estimation of parameters in domains where data contain misclassification and measurement errors1994Doctoral thesis, monograph (Other academic)
• 45.
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Mathematics.
Stochastic epidemic models and their statistical analysis2000In: Springer Lecture Notes in Statistics, Vol. 151Book (Refereed)
• 46.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
Houghtransformen – ett verktyg för bildigenkänning2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 47.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Testing For Normality of Censored Data2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

In order to make statistical inference, that is drawing conclusions from a sample to describe a population, it is crucial to know the correct distribution of the data. This paper focused on censored data from the normal distribution. The purpose of this paper was to answer whether we can test if data comes from a censored normal distribution. This by using normality tests and tests designed for censored data and investigate if we got correct size of these tests. This has been carried out with simulations in the program R for left censored data. The results indicated that with increasing censoring normality tests failed to accept normality in a sample. On the other hand the censoring tests met the requirements with increasing censoring level, which was the most important conclusion in this paper.

• 48.
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.
An improvement of the GPH estimator1999Report (Other scientific)
• 49.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
Maximum likelihood estimation of the normal inverse Gaussian stochastic volatility model1999Report (Other scientific)
• 50.
Uppsala University, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Faculty of Social Sciences, Department of Information Science.
Modeling and forecasting with the normal inverse Gaussian stochastic volatility model1999Report (Other scientific)
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