TY - JOUR

T1 - Maximum Average-Power (MAP) tests

AU - Chen, Lin An

AU - Hung, Hui-Nien

AU - Chen, Chih-Rung

PY - 2007/9

Y1 - 2007/9

N2 - 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.

AB - 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.

KW - Maximum average-power test

KW - Most Powerful test

KW - Uniformly most powerful test

KW - Uniformly most powerful unbiased test

UR - http://www.scopus.com/inward/record.url?scp=34548356925&partnerID=8YFLogxK

U2 - 10.1080/03610920701215480

DO - 10.1080/03610920701215480

M3 - Article

AN - SCOPUS:34548356925

SN - 0361-0926

VL - 36

SP - 2237

EP - 2249

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 12

ER -