A class of tests for a general covariance structure

Hirofumi Wakaki, Shinto Eguchi and Yasunori Fujikoshi

Journal of Multivariate Analysis, 1990, vol. 32, issue 2, 313-325

Abstract: Let S be a p - p random matrix having a Wishart distribution Wp(n,n-1[Sigma]). For testing a general covariance structure [Sigma] = [Sigma]([xi]), we consider a class of test statistics Th = n inf [varrho]h(S, [Sigma]([xi])), where [varrho]h([Sigma]1, [Sigma]2) = [Sigma]j = 1ph([lambda]j) is a distance measure from [Sigma]1 to [Sigma]2, [lambda]i's are the eigenvalues of [Sigma]1[Sigma]2-1, and h is a given function with certain properties. This paper gives an asymptotic expansion of the null distribution of Th up to the order n-1. Using the general asymptotic formula, we give a condition for Th to have a Bartlett adjustment factor. Two special cases are considered in detail when [Sigma] is a linear combination or [Sigma]-1 is a linear combination of given matrices.

Keywords: asymptotic; expansion; class; of; test; statistics; general; covariance; structure; linear; structure; null; distribution (search for similar items in EconPapers)
Date: 1990
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Citations: View citations in EconPapers (6)

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