On UMPS hypothesis testing

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Davy Paindaveine
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引用次数: 0

Abstract

For two-sided hypothesis testing in location families, the classical optimality criterion is the one leading to uniformly most powerful unbiased (UMPU) tests. Such optimal tests, however, are constructed in exponential models only. We argue that if the base distribution is symmetric, then it is natural to consider uniformly most powerful symmetric (UMPS) tests, that is, tests that are uniformly most powerful in the class of level-\(\alpha \) tests whose power function is symmetric. For single-observation models, we provide a condition ensuring existence of UMPS tests and give their explicit form. When this condition is not met, UMPS tests may fail to exist and we provide a weaker condition under which there exist UMP tests in the class of level-\(\alpha \) tests whose power function is symmetric and U-shaped. In the multi-observation case, we obtain results in exponential models that also allow for non-location families.

Abstract Image

关于UMPS假设检验
对于位置族的双侧假设检验,经典的最优性准则是导致一致最有力无偏检验的准则。然而,这种最优测试只能在指数模型中构建。我们认为,如果基本分布是对称的,那么很自然地考虑一致最强大的对称(UMPS)测试,即在幂函数是对称的level- \(\alpha \)测试类中一致最强大的测试。对于单观测模型,给出了UMPS检验存在的条件,并给出了其显式形式。当不满足此条件时,UMPS测试可能不存在,我们提供了一个较弱的条件,即在幂函数为对称u型的水平- \(\alpha \)测试类中存在UMP测试。在多观测情况下,我们得到了指数模型的结果,也允许非位置族。
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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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