A Necessary Test of Goodness of Fit for Sphericity

K. T. Fang, Lixing Zhu and P. M. Bentler

Journal of Multivariate Analysis, 1993, vol. 45, issue 1, 34-55

Abstract: A p - 1 random vector x is said to have a spherical distribution, if for every p - p orthogonal matrix Q, x and Qx have the same distribution. In this paper, some nonparametric goodness of fit Wilcoxon-type tests for sphericity are proposed. Some results on the limiting distributions of the statistics are obtained. These results provide a theoretical basis for a necessary test of sphericity.

Date: 1993
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