Maximum Average-Power (MAP) tests

Lin An Chen*, Hui-Nien Hung, Chih-Rung Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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.

Original languageEnglish
Pages (from-to)2237-2249
Number of pages13
JournalCommunications in Statistics - Theory and Methods
Issue number12
StatePublished - Sep 2007


  • Maximum average-power test
  • Most Powerful test
  • Uniformly most powerful test
  • Uniformly most powerful unbiased test


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