On the limiting distributions of multivariate depth-based rank sum statistics and related tests

• 成果类型: Article
• 署名作者: Zu, Yijun; He, Xuming
• 署名单位: Michigan State University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000876
• 发表日期: 2006
• 页码: 2879-2896
• 关键词: convergence; THEOREM

摘要

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.