Hypothesis Testing for Independence Under Blocked Compound Symmetric Covariance Structure

Hypothesis Testing for Independence Under Blocked Compound Symmetric Covariance Structure One type of covariance structure is known as blocked compound symmetry. Recently, Roy et al. (J Multivar Anal 144:81–90, 2016) showed that, assuming this covariance structure, unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem. In this paper, we derive the distributions of unbiased estimators and consider hypothesis testing for independence. Representative test statistics such as the likelihood ratio criterion, Wald statistic, Rao’s score statistic, and gradient statistic are derived, and we evaluate the accuracy of the test using these statistics through numerical simulations. The power of the Wald test is the largest when the dimension is high, and the power of the likelihood ratio test is the largest when the dimension is low. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics and Statistics Springer Journals

Hypothesis Testing for Independence Under Blocked Compound Symmetric Covariance Structure

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Publisher
Springer Journals
Copyright
Copyright © 2018 by School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general; Statistics, general
ISSN
2194-6701
eISSN
2194-671X
D.O.I.
10.1007/s40304-018-0130-4
Publisher site
See Article on Publisher Site

Abstract

One type of covariance structure is known as blocked compound symmetry. Recently, Roy et al. (J Multivar Anal 144:81–90, 2016) showed that, assuming this covariance structure, unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem. In this paper, we derive the distributions of unbiased estimators and consider hypothesis testing for independence. Representative test statistics such as the likelihood ratio criterion, Wald statistic, Rao’s score statistic, and gradient statistic are derived, and we evaluate the accuracy of the test using these statistics through numerical simulations. The power of the Wald test is the largest when the dimension is high, and the power of the likelihood ratio test is the largest when the dimension is low.

Journal

Communications in Mathematics and StatisticsSpringer Journals

Published: Apr 30, 2018

References

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