Title

Testing For Elliptical Symmetry In Covariance-Matrix-Based Analyses

Keywords

Elliptical distribution; Matrix of fourth-order moments; Wald statistic

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. © 2002 Elsevier Science B.V. All rights reserved.

Publication Date

12-15-2002

Publication Title

Statistics and Probability Letters

Volume

60

Issue

4

Number of Pages

395-404

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0167-7152(02)00306-1

Socpus ID

0037114392 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0037114392

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