Score test for a separable covariance structure with the first component as compound symmetric correlation matrix

Katarzyna Filipiak, Daniel Clein and Anuradha Roy
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Daniel Clein: P. J. Safarik University
Anuradha Roy: UTSA

Working Papers from College of Business, University of Texas at San Antonio

Abstract: Likelihood ratio tests (LRTs) for separability of a covariance structure for doubly multivariate data are widely studied in the literature. There are three types of LRT: biased tests based on an asymptotic chi-square null distribution; unbiased/unmodied tests based on an empirical null distribution; and unbiased/modied tests with a test statistic modied to follow a theoretical chi-square null distribution. The Rao's score test (RST) statistic, an alternative for both bi-ased and unbiased/unmodied versions of the corresponding LRT test statistics are derived fora common case. The separability of a covariance structure with the rst component as a com-pound symmetric correlation matrix under the assumption of multivariate normality is tested. Simulation studies compare the biased LRT to biased RST, and unbiased/unmodied LRT to unbiased/unmodied RST. The RSTs outperform their corresponding LRTs in general. Three ex-amples are presented. Since the RST does not require estimation of a general variance-covariance matrix (the alternative hypothesis), this test can be performed for small sample sizes, where the variance-covariance matrix could not be estimated for the corresponding LRT, making the LRT infeasible. In cases where both LRT and RST are feasible, the RST outperforms a comparable LRT.

Keywords: Empirical null distribution; Likelihood ratio test; Maximum likelihood estimates; Rao's score test; Separable covariance structure (search for similar items in EconPapers)
JEL-codes: H12 H19 (search for similar items in EconPapers)
Pages: 43 pages
Date: 2015-03-03
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Published in Review of Economics, March 1999, pages 1-23

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