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Ahmad, M. Rauf
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Publications (10 of 17) Show all publications
Ahmad, M. R. (2019). A significance test of the RV coefficient in high dimensions. Computational Statistics & Data Analysis, 131, 116-130
Open this publication in new window or tab >>A significance test of the RV coefficient in high dimensions
2019 (English)In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 131, p. 116-130Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2019
Keywords
RV coefficient, Dependency measure, Cross-correlations, High-dimensional inference
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-371105 (URN)10.1016/j.csda.2018.10.008 (DOI)000450384700011 ()
Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2018-12-20Bibliographically approved
Ahmad, M. R. (2019). Multiple comparisons of mean vectors with large dimension under general conditions. Journal of Statistical Computation and Simulation, 89(6), 1044-1059
Open this publication in new window or tab >>Multiple comparisons of mean vectors with large dimension under general conditions
2019 (English)In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, no 6, p. 1044-1059Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Taylor & Francis, 2019
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-375557 (URN)10.1080/00949655.2019.1572147 (DOI)000460629700007 ()
Available from: 2019-01-31 Created: 2019-01-31 Last updated: 2019-03-25Bibliographically approved
Ahmad, M. R. (2019). Tests of Zero Correlation Using Modified RV Coefficient for High-Dimensional Vectors. Journal of Statistical Theory and Practice, 13(3), Article ID 43.
Open this publication in new window or tab >>Tests of Zero Correlation Using Modified RV Coefficient for High-Dimensional Vectors
2019 (English)In: Journal of Statistical Theory and Practice, ISSN 1559-8608, E-ISSN 1559-8616, Vol. 13, no 3, article id 43Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS AS, 2019
Keywords
Block-diagonal structure, Cross-correlations, High-dimensional inference
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-384981 (URN)10.1007/s42519-019-0043-x (DOI)000467553400002 ()
Available from: 2019-06-14 Created: 2019-06-14 Last updated: 2019-06-14Bibliographically approved
Ahmad, M. R. (2018). A homogeneity test of large dimensional covariance matrices under non-normality. Kybernetika (Praha), 54(5), 908-920
Open this publication in new window or tab >>A homogeneity test of large dimensional covariance matrices under non-normality
2018 (English)In: Kybernetika (Praha), ISSN 0023-5954, E-ISSN 1805-949X, Vol. 54, no 5, p. 908-920Article in journal (Refereed) Published
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.

Keywords
high-dimensional inference, covariance testing, U-statistics, non-normality
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-375789 (URN)10.14736/kyb-2018-5-0908 (DOI)000455560300003 ()
Available from: 2019-02-01 Created: 2019-02-01 Last updated: 2019-02-01Bibliographically approved
Ahmad, M. R. & Pavlenko, T. (2018). A U-classifier for high-dimensional data under non-normality. Journal of Multivariate Analysis, 167, 269-283
Open this publication in new window or tab >>A U-classifier for high-dimensional data under non-normality
2018 (English)In: Journal of Multivariate Analysis, ISSN 0047-259X, E-ISSN 1095-7243, Vol. 167, p. 269-283Article in journal (Refereed) Published
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.

Keywords
Bias-adjusted classifier, High-dimensional classification, U-statistics
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-362640 (URN)10.1016/j.jmva.2018.05.008 (DOI)000441371100017 ()
Funder
Swedish Research Council, 2013-45266
Available from: 2018-10-09 Created: 2018-10-09 Last updated: 2018-10-09Bibliographically approved
Ahmad, M. R. (2017). Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension. Scandinavian Journal of Statistics, 44(2), 500-523
Open this publication in new window or tab >>Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension
2017 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 44, no 2, p. 500-523Article in journal (Refereed) Published
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.

Keywords
high-dimensional inference, multi-sample sphericity, U-statistics
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-325684 (URN)10.1111/sjos.12262 (DOI)000400985000010 ()
Available from: 2017-07-06 Created: 2017-07-06 Last updated: 2017-07-06Bibliographically approved
Ahmad, M. R. (2017). Location-invariant tests of homogeneity of large-dimensional covariance matrices. Journal of Statistical Theory and Practice, 11(4), 731-745
Open this publication in new window or tab >>Location-invariant tests of homogeneity of large-dimensional covariance matrices
2017 (English)In: Journal of Statistical Theory and Practice, ISSN 1559-8608, E-ISSN 1559-8616, Vol. 11, no 4, p. 731-745Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2017
Keywords
Covariance matrices, multivariate inference, homogeneity tests, high-dimensional theory
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-345227 (URN)10.1080/15598608.2017.1308895 (DOI)000423985000012 ()
Available from: 2018-03-09 Created: 2018-03-09 Last updated: 2018-03-09Bibliographically approved
Zwanzig, S. & Ahmad, M. R. (2017). On the behavior of the risk of a LASSO-type estimator. In: Antoch J., Jurečková J., Maciak M., Pešta M. (Ed.), Analytical Methods in Statistics, Amistat 2015: . Paper presented at Workshop on Analytical Methods in Statistics (AMISTAT), , Prague, CZECH REPUBLIC, November 10-13, 2015 (pp. 189-207). Springer
Open this publication in new window or tab >>On the behavior of the risk of a LASSO-type estimator
2017 (English)In: Analytical Methods in Statistics, Amistat 2015, Springer, 2017, p. 189-207Conference paper, Published paper (Refereed)
Abstract [en]

We introduce a LASSO-type estimator as a generalization of the classical LASSO estimator for non-orthogonal design. The generalization, named the SVDLASSO,allows the design matrix to be of less than full rank.We assume fixed design matrix and normality but otherwise the properties of the SVD-LASSO do not necessarily rest on any strong conditions, particularly sparsity.We derive exact expressions for the risk of the SVD-LASSO and compare it with that of the corresponding ridge estimator.

Place, publisher, year, edition, pages
Springer, 2017
Series
Springer Proceedings in Mathematics & Statistics, E-ISSN 2194-1009 ; 193
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-371622 (URN)10.1007/978-3-319-51313-3_9 (DOI)000407479100009 ()978-3-319-51312-6 (ISBN)978-3-319-51313-3 (ISBN)
Conference
Workshop on Analytical Methods in Statistics (AMISTAT), , Prague, CZECH REPUBLIC, November 10-13, 2015
Available from: 2018-12-21 Created: 2018-12-21 Last updated: 2019-02-25Bibliographically approved
Ahmad, M. R. (2017). Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality. Communications in Statistics - Theory and Methods, 46(8), 3738-3753
Open this publication in new window or tab >>Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data under non-normality
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 46, no 8, p. 3738-3753Article in journal (Refereed) Published
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.

Keywords
High-dimensionality, multi-sample sphericity, non-normality, U-statistics, 62H15
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-316050 (URN)10.1080/03610926.2015.1073310 (DOI)000392413900010 ()
Available from: 2017-02-23 Created: 2017-02-23 Last updated: 2017-11-29Bibliographically approved
Ahmad, M. R. (2017). Tests for independence of vectors with large dimension.
Open this publication in new window or tab >>Tests for independence of vectors with large dimension
2017 (English)Report (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.

Publisher
p. 25
Series
Working paper / Department of Statistics, Uppsala University ; 2017:1
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-312578 (URN)
Available from: 2017-01-11 Created: 2017-01-11 Last updated: 2017-04-27Bibliographically approved
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