The asymptotic equivalence of Bayes and maximum likelihood estimation |
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Authors: | Helmut Strasser |
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Institution: | Institute for Socio-Economic Development, Academy of Sciences, 1010 Vienna, Austria |
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Abstract: | Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav 3], and Ibragimov and Has'minskii 4], as far as the speed of convergence is concerned. |
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Keywords: | 62H99 Maximum likelihood estimation Bayes estimation limit theorems speed of convergence |
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