Title

Testing for elliptical symmetry in covariance-matrix-based analyses

Authors

Authors

J. R. Schott

Abbreviated Journal Title

Stat. Probab. Lett.

Keywords

elliptical distribution; matrix of fourth-order moments; Wald statistic; MULTIVARIATE; Statistics & Probability

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. (C) 2002 Elsevier Science B.V. All rights reserved.

Journal Title

Statistics & Probability Letters

Volume

60

Issue/Number

4

Publication Date

1-1-2002

Document Type

Article

Language

English

First Page

395

Last Page

404

WOS Identifier

WOS:000179625700007

ISSN

0167-7152

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