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

Author

Listed:
  • Katarzyna Filipiak
  • Daniel Klein

    (P. J. Safarik University)

  • Anuradha Roy

    (UTSA)

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.

Suggested Citation

  • Katarzyna Filipiak & Daniel Klein & Anuradha Roy, 2015. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Working Papers 0148mss, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0148mss
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    References listed on IDEAS

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    More about this item

    Keywords

    Empirical null distribution; Likelihood ratio test; Maximum likelihood estimates; Rao's score test; Separable covariance structure;
    All these keywords.

    JEL classification:

    • H12 - Public Economics - - Structure and Scope of Government - - - Crisis Management
    • H19 - Public Economics - - Structure and Scope of Government - - - Other

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