Title: Maximum average-power (MAP) tests
Authors: Chen, Lin-An
Hung, Hui-Nien
Chen, Chih-Rung
Institute of Statistics
Keywords: maximum average-power test;most powerful test;uniformly most powerful test;uniformly most powerful unbiased test
Issue Date: 2007
Abstract: The objective of this article is to propose and study frequentist tests that have maximum average power, averaging with respect to some specified weight function. First, some relationships between these tests, called maximum average-power (MAP) tests, and most powerful or uniformly most powerful tests are presented. Second, the existence of a maximum average-power test for any hypothesis testing problem is shown. Third, an MAP test for any hypothesis testing problem with a simple null hypothesis is constructed, including some interesting classical examples. Fourth, an MAP test for a hypothesis testing problem with a composite null hypothesis is discussed. From any one-parameter exponential family, a commonly used UMPU test is shown to be also an MAP test with respect to a rich class of weight functions. Finally, some remarks are given to conclude the article.
URI: http://hdl.handle.net/11536/5746
ISSN: 0361-0926
DOI: 10.1080/03610920701215480
Volume: 36
Issue: 9-12
Begin Page: 2237
End Page: 2249
Appears in Collections:Conferences Paper

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