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Testing for elliptical symmetry in covariance-matrix-based analyses

โœ Scribed by James R. Schott

Book ID
104301988
Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
126 KB
Volume
60
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

Asymptotic Distributions of Some Test Cr
Asymptotic Distributions of Some Test Criteria for the Covariance Matrix in Elliptical Distributions under Local Alternatives
โœ S. Purkayastha; M.S. Srivastava ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 598 KB

The asymptotic distributions under local alternatives of two test criteria for testing the hypothesis that the characteristic roots of the covariance matrix of an elliptical population, assumed distinct, are equal to a set of specified numbers, are derived. The two tests are the modified likelihood