Hypothesis Testing for Independence Under Blocked Compound Symmetric Covariance Structure

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.

Keywords

Hypothesis testing / Asymptotic distribution / Independence / Blocked compound symmetric covariance structure