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The asymptotic equivalence of Bayes and maximum likelihood estimation

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  • Strasser, Helmut

Abstract

Let (X, ) be a measurable space, [Theta] [subset, double equals] an open interval and P[Omega] [short parallel] , [Omega] [epsilon] [Theta], a family of probability measures fulfilling certain regularity conditions. Let [Omega]n be the maximum likelihood estimate for the sample size n. Let [lambda] be a prior distribution on [Theta] 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 [lambda] and L for the sample size n. It is proved that for every compact K [subset, double equals] [Theta] 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.

Suggested Citation

  • Strasser, Helmut, 1975. "The asymptotic equivalence of Bayes and maximum likelihood estimation," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 206-226, June.
    • Handle: RePEc:eee:jmvana:v:5:y:1975:i:2:p:206-226
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    Cited by:

    1. Abraham, Christophe, 2005. "Asymptotics in Bayesian decision theory with applications to global robustness," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 50-65, July.

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