Asymptotic approximations to the Bayes posterior risk. (1990) - Zoubeidi, Toufik
Abstract : Suppose that, given ω = ( ω 1, ω 2 ) ∈ ℜ 2, X 1, X 2, … and Y 1, Y 2, … are independent random variables and their respective distribution functions G ω 1 and G ω 2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω 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 H 0 : ω ∈ Ω 1 versus H 1 : ω ∈ Ω 2 using a zero-one loss function, where Ω 1 and Ω 2 are disjoint closed convex subsets of the parameter space.