Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions

Carlos A. Coelho () and Anuradha Roy
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Carlos A. Coelho: Universidade Nova de Lisboa
Anuradha Roy: The University of Texas at San Antonio

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 26, issue 2, No 4, 308-330

Abstract: Abstract In this paper, the authors study the problem of testing the hypothesis of a block compound symmetry covariance matrix with two-level multivariate observations, taken for m variables over u sites or time points. Through the use of a suitable block-diagonalization of the hypothesis matrix, it is possible to obtain a decomposition of the main hypothesis into two sub-hypotheses. Using this decomposition, it is then possible to obtain the likelihood ratio test statistic as well as its exact moments in a much simpler way. The exact distribution of the likelihood ratio test statistic is then analyzed. Because this distribution is quite elaborate, yielding a non-manageable distribution function, a manageable but very precise near-exact distribution is developed. Numerical studies conducted to evaluate the closeness between this near-exact distribution and the exact distribution show the very good performance of this approximation even for very small sample sizes and the approach followed allows us to extend its validity to situations where the population distributions are elliptically contoured. A real-data example is presented and a simulation study is also conducted.

Keywords: Beta random variables; Characteristic function; Composition of hypotheses; Likelihood ratio statistic; Near-exact distributions; Product distribution; 62H15; 62H10; 62E15; 62E20; 62E10; 60E10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11749-016-0512-4

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