Testing for elliptical symmetry in covariance-matrix-based analyses

    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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