摘要翻译:
Liu和Singh[J.Amer.Statist.Assoc.88(1993)252-260]作为Wilcoxon秩和统计量对单变量数据的推广,提出了一种基于深度的多元数据秩和统计量,已用于质量控制和实验研究中的多元秩检验。然而,这些应用是基于由Liu和Singh提供的一个推测的极限分布[J.Amer.Statist.Assoc.88(1993)252-260]。本文在一般正则性条件下证明了该猜想,从而验证了秩和统计量在文献中的各种应用。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中的位置-尺度变化方面具有更强的能力。
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英文标题:
《On the limiting distributions of multivariate depth-based rank sum
statistics and related tests》
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作者:
Yijun Zuo, Xuming He
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
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.
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PDF链接:
https://arxiv.org/pdf/708.0167