A characterization of maximin tests for two composite hypotheses

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• 作者：A. Gushchin
• 关键词：dual problem ; testing composite hypotheses ; maximin test ; 62F03 ; 62G10
• 刊名：Mathematical Methods of Statistics
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：24
• 期：2
• 页码：110-121
• 全文大小：631 KB
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• 作者单位：A. Gushchin (1) (2)
  
  1. Steklov Mathematical Institute, Moscow, Russia
  2. International Laboratory of Quantitative Finance, National Research Univ. Higher School of Economics, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistical Theory and Methods
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-8045

文摘

We consider the problem of testing two composite hypotheses in the minimax setting. To find maximin tests, we propose a new dual optimization problem which has a solution under a mild additional assumption. This allows us to characterize maximin tests in considerable generality. We give a simple example where the null hypothesis and the alternative are strictly separated, however, a maximin test is purely randomized.