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December 2006 On the limiting distributions of multivariate depth-based rank sum statistics and related tests
Yijun Zuo, Xuming He
Ann. Statist. 34(6): 2879-2896 (December 2006). DOI: 10.1214/009053606000000876

Abstract

A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252–260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests in quality control and in experimental studies. Those applications, however, are based on a conjectured limiting distribution, provided by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252–260]. The present paper proves the conjecture under general regularity conditions and, therefore, validates various applications of the rank sum statistic in the literature. The paper also shows that the corresponding rank sum tests can be more powerful than Hotelling’s T2 test and some commonly used multivariate rank tests in detecting location-scale changes in multivariate distributions.

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Yijun Zuo. Xuming He. "On the limiting distributions of multivariate depth-based rank sum statistics and related tests." Ann. Statist. 34 (6) 2879 - 2896, December 2006. https://doi.org/10.1214/009053606000000876

Information

Published: December 2006
First available in Project Euclid: 23 May 2007

zbMATH: 1114.62020
MathSciNet: MR2329471
Digital Object Identifier: 10.1214/009053606000000876

Subjects:
Primary: 62G20
Secondary: 62G10, 62H10, 62H15

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 6 • December 2006
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