On the limiting distributions of multivariate depth-based rank sum statistics and related tests
On the limiting distributions of multivariate depth-based rank sum statistics and related tests
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DOI：
10.1214/009053606000000876
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发表时间：
2006-12-01
影响因子：
4.5
通讯作者：
He, Xuming
中科院分区：
文献类型：
--
作者：
Zu, Yijun;He, Xuming
基于深度的多元数据秩和统计量[J]。阿米尔。中央集权。Assoc. 88(1993) 252-260]作为对单变量数据的Wilcoxon秩和统计量的扩展，已用于质量控制和实验研究中的多变量秩检验。然而，这些应用是基于Liu和Singh [J]提供的一个推测的极限分布。阿米尔-集权。中华医学会杂志。88(1993)252-260。本文在一般正则性条件下证明了这个猜想，从而验证了文献中秩和统计量的各种应用。本文还表明，相应的秩和检验比Hotelling的T-2检验和一些常用的多元秩检验在检测多元分布的位置尺度变化方面更有效。
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.