Admissibility of unbiased tests for a composite hypothesis with a restricted alternative |
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Authors: | Manabu Iwasa |
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Affiliation: | (1) Department of Mathematical Science, Osaka University, 560 Toyonaka, Osaka, Japan |
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Abstract: | This paper discusses -admissiblility and d-admissiblity which are important concepts in studying the performance of statistical tests for composite hypotheses. A sufficient condition for -admissibility is presented. When =1/m, the Nomakuchi-Sakata test, which is uniformly more powerful than the likelihood ratio test for hypotheses min (1, 1) = 0 versus min (1, 1) > 0, is generalized for a class of distributions in an exponential family, and its unbiasedness and -admissibility are shown. Finally, the case of 1/m is discussed in brief. |
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Keywords: | Nomakuchi-Sakata test /content/l2xt14447q704671/xxlarge945.gif" alt=" agr" align=" BASELINE" BORDER=" 0" >-admissibility d-admissibility unbiasedness exponential family completeness |
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