Abstract
This paper discusses α-admissiblility and d-admissiblity which are important concepts in studying the performance of statistical tests for composite hypotheses. A sufficient condition for α-admissibility is presented. When α=1/m, the Nomakuchi-Sakata test, which is uniformly more powerful than the likelihood ratio test for hypotheses min (θ1, θ1) = 0 versus min (θ1, θ1) > 0, is generalized for a class of distributions in an exponential family, and its unbiasedness and α-admissibility are shown. Finally, the case of α≠ 1/m is discussed in brief.
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Iwasa, M. Admissibility of unbiased tests for a composite hypothesis with a restricted alternative. Ann Inst Stat Math 43, 657–665 (1991). https://doi.org/10.1007/BF00121645
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DOI: https://doi.org/10.1007/BF00121645