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The testing problems of hypothesis of k sample approximate equality in the presence of gross errors

存在粗差情况下k样本近似相等假设的检验问题

基本信息

批准号：
14580347
负责人：
KAKIUCHI Itsuro
金额：
$ 1.92万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14580347/
关键词：
Hypothesis of approximate equality Robust test k-sample rank test Gross error neighborhood Majorization Weak majorization Slippage problem of location Majorization Slippage test of location Robustness Clustering Design of experiments

项目摘要

We extend the classical nonparametric hypothesis of k sample equality to a hypothesis of k sample approximate equality and explore the asymptotic properties of sequences of rank tests under a k-sample local asymptotic gross error model. Our results reveal that the classical optimum rank tests are sensitive to deviation from the assumptions of rather stringent equality, and hence their use is dangerous in practical situations where deviation may occur. The study of the robustness of rank tests for k-sample approximate equality is also important from the point of view of practical applications, and then the majorization methods can be quite effectively utilized for constructing asymptotic level α rank tests and giving the lower bounds for their asymptotic minimum powers. We should emphasize that the new ideas and majorization devices developed in this paper are essential for overcoming the peculiar difficulties arising in the k-sample case.A robust slippage test problem of k location parameters in the presence of gross errors is formulated from the point of view of Huber's robust test theory. Under an asymptotic model of the robust slippage test problem an asymptotic level α slippage rank test based on k linear rank statistics is constructed by applying majorization methods and its asymptotic minimum power evaluated by applying weak majorization methods. It is also shown that the slippage rank test is asymptotically unbiased.

将经典的k样本相等的非参数假设推广到k样本近似相等的假设，探讨了k样本局部渐近粗误差模型下秩检验序列的渐近性质。我们的结果表明，经典的最优秩检验对偏离相当严格的平等假设是敏感的，因此在可能发生偏差的实际情况下使用它们是危险的。从实际应用的角度来看，研究k-样本近似相等的秩检验的鲁棒性也很重要，然后利用多数化方法可以很有效地构造渐近水平α秩检验并给出其渐近最小幂的下界。我们应该强调，本文中提出的新思想和多数化装置对于克服k样本情况下出现的特殊困难是必不可少的。从Huber鲁棒性试验理论出发，提出了存在粗误差情况下k个位置参数的鲁棒性滑移试验问题。在鲁棒滑移检验问题的渐近模型下，应用最优化方法构造了基于k个线性秩统计量的渐近水平α滑移秩检验，并利用弱最优化方法求了其渐近最小幂。还证明了滑移秩检验是渐近无偏的。