Testing for elliptical symmetry in covariance-matrix-based analyses

James R. Schott

Statistics & Probability Letters, 2002, vol. 60, issue 4, 395-404

Abstract: Many normal-theory test procedures for covariance matrices remain valid outside the family of normal distributions if the matrix of fourth-order moments has structure similar to that of a normal distribution. In particular, for elliptical distributions this matrix of fourth-order moments is a scalar multiple of that for the normal, and for this reason many normal-theory statistics can be adjusted by a scalar multiple so as to retain their asymptotic distributional properties across elliptical distributions. For these analyses, a test for the validity of these scalar-adjusted normal-theory procedures can be viewed as a test on the structure of the matrix of fourth-order moments. In this paper, we develop a Wald statistic for conducting such a test.

Keywords: Elliptical; distribution; Matrix; of; fourth-order; moments; Wald; statistic (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (12)

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