On the limiting distributions of multivariate depth-based rank sum statistics and related tests. (English) Zbl 1114.62020

Zuo, Yijun; He, Xuming

Ann. Stat. 34, No. 6, 2879-2896 (2006).

Summary: A depth-based rank sum statistic for multivariate data introduced by R. Y. Liu and K. Singh [J. Am. Stat. Assoc. 88, No. 421, 252–260 (1993; Zbl 0772.62031)] 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 (op. cit.).
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 \(T^2\) test and some commonly used multivariate rank tests in detecting location-scale changes in multivariate distributions.

MSC:

62E20	Asymptotic distribution theory in statistics
62G10	Nonparametric hypothesis testing
62H15	Hypothesis testing in multivariate analysis
62H10	Multivariate distribution of statistics
62G20	Asymptotic properties of nonparametric inference

Citations:

Zbl 0772.62031

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