On the limiting distributions of multivariate depth-based rank sum statistics and related tests
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 T^2 test and some commonly used multivariate rank tests in detecting location-scale changes in multivariate distributions.
Cite
@article{arxiv.0708.0167,
title = {On the limiting distributions of multivariate depth-based rank sum statistics and related tests},
author = {Yijun Zuo and Xuming He},
journal= {arXiv preprint arXiv:0708.0167},
year = {2011}
}
Comments
Published at http://dx.doi.org/10.1214/009053606000000876 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)