Testing For Elliptical Symmetry In Covariance-Matrix-Based Analyses
Elliptical distribution; Matrix of fourth-order moments; Wald statistic
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.
Statistics and Probability Letters
Number of Pages
Source API URL
Schott, James R., "Testing For Elliptical Symmetry In Covariance-Matrix-Based Analyses" (2002). Scopus Export 2000s. 2243.