Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 2, Pages 99-116
Asymptotic approximations to the Bayes posterior risk
Department of Statistics, University of Rochester, Rochester 14627, NY, USA
Received 1 January 1990; Revised 1 March 1990
Copyright © 1990 Toufik Zoubeidi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Suppose that, given , and
are independent random variables and their respective
distribution functions and belong to a one parameter
exponential family of distributions. We derive approximations
to the posterior probabilities of lying in closed convex subsets
of the parameter space under a general prior density. Using
this, we then approximate the Bayes posterior risk for testing
the hypotheses versus using a zero-one
loss function, where and are disjoint closed convex subsets
of the parameter space.