Asymptotic approximations to the Bayes posterior risk

Toufik Zoubeidi

International Journal of Stochastic Analysis, 1990, vol. 3, 1-18

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.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:818246

DOI: 10.1155/S1048953390000090

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