ADMISSIBILITY OF UNBIASED TESTS FOR A COMPOSITE HYPOTHESIS WITH A RESTRICTED ALTERNATIVE

MANABU IWASA

Department of Mathematical Science, Osaka University, Toyonaka, Osaka 560, Japan

(Received November 29, 1989; revised November 1, 1990)

Abstract. This paper discusses α-admissibility and d-admissibility 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(θ_{1}, θ_{2}) = 0 versus min(θ_{1}, θ_{2}) > 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.

Key words and phrases: Nomakuchi-Sakata test, α-admissibility, d-admissi-bility, unbiasedness, exponential family, completeness.