Journal
STATISTICS & PROBABILITY LETTERS
Volume 60, Issue 4, Pages 395-404Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/S0167-7152(02)00306-1
Keywords
elliptical distribution; matrix of fourth-order moments; Wald statistic
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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.
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