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

28 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

User-Defined Keywords

Goodness of fit
Nonparametric
Wilcoxon statistics

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10.1006/jmva.1993.1025

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title = "A necessary test of goodness of fit for sphericity",

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.",

keywords = "Goodness of fit, Nonparametric, Wilcoxon statistics",

author = "Fang, \{Kai Tai\} and Lixing Zhu and Bentler, \{Peter M.\}",

note = "This work was supported by U.S. National Institute on Drug Abuse Grant DA01070 and Hong Kong UPGC Grant.",

year = "1993",

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AU - Zhu, Lixing

AU - Bentler, Peter M.

N1 - This work was supported by U.S. National Institute on Drug Abuse Grant DA01070 and Hong Kong UPGC Grant.

PY - 1993/4

Y1 - 1993/4

N2 - 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.

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.

KW - Goodness of fit

KW - Nonparametric

KW - Wilcoxon statistics

UR - https://www.scopus.com/pages/publications/0002738228

U2 - 10.1006/jmva.1993.1025

DO - 10.1006/jmva.1993.1025

M3 - Journal article

AN - SCOPUS:0002738228

SN - 0047-259X

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SP - 34

EP - 55

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

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ER -

A necessary test of goodness of fit for sphericity

Abstract

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