(Received November 29, 1989; revised November 1, 1990)
Abstract. This paper discusses alpha-admissibility and d-admissibility which are important concepts in studying the performance of statistical tests for composite hypotheses. A sufficient condition for alpha-admissibility is presented. When alpha = 1/m, the Nomakuchi-Sakata test, which is uniformly more powerful than the likelihood ratio test for hypotheses min(theta1,theta2) = 0 versus min(theta1,theta2) > 0, is generalized for a class of distributions in an exponential family, and its unbiasedness and alpha-admissibility are shown. Finally, the case of alpha \neq 1/m is discussed in brief.
Key words and phrases: Nomakuchi-Sakata test, alpha-admissibility, d-admissibility, unbiasedness, exponential family, completeness.
Source ( TeX , DVI , PS )