A necessary test of goodness of fit for sphericity

Kai Tai Fang; Lixing Zhu; Peter M. Bentler

doi:10.1006/jmva.1993.1025

A necessary test of goodness of fit for sphericity

Kai Tai Fang, Lixing Zhu, Peter M. Bentler

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

26 Citations (Scopus)

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.

Original language	English
Pages (from-to)	34-55
Number of pages	22
Journal	Journal of Multivariate Analysis
Volume	45
Issue number	1
DOIs	https://doi.org/10.1006/jmva.1993.1025
Publication status	Published - Apr 1993

Scopus Subject Areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

User-Defined Keywords

Goodness of fit
Nonparametric
Wilcoxon statistics

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10.1006/jmva.1993.1025

Cite this

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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.",

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AU - Bentler, Peter M.

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AB - 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.

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A necessary test of goodness of fit for sphericity

Abstract

Scopus Subject Areas

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