The asymptotic equivalence of Bayes and maximum likelihood estimation

Helmut Strasser

Journal of Multivariate Analysis, 1975, vol. 5, issue 2, 206-226

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.

Keywords: Maximum; likelihood; estimation; Bayes; estimation; limit; theorems; speed; of; convergence (search for similar items in EconPapers)
Date: 1975
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