ON THE ASYMPTOTIC DEFECT OF SOME BAYESIAN CRITERIA

摘要

This paper focuses on the problem of testing a simple hypothesis about a one-dimensional parameter against onesided alternatives with independent identically distributed random variables. A formula for extreme deviation of the power function from the envelope power function is obtained for asymptotically efficient Bayesian criteria based on a Bayesian likelihood ratio. This formula makes it possible to find the asymptotic deficiency in terms of the Hodges-Lehmann deficiency. The method used here makes it possible to relax necessary regularity conditions.