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Informationtheoretic asymptotics of Bayes methods
 IEEE Transactions on Information Theory
, 1990
"... AbstractIn the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior. We examine the relative entropy distance D,, between the true density and the Bayesian densit ..."
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Cited by 107 (10 self)
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AbstractIn the absence of knowledge of the true density function, Bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior. We examine the relative entropy distance D,, between the true density and the Bayesian density and show that the asymptotic distance is (d/2Xlogn)+ c, where d is the dimension of the parameter vector. Therefore, the relative entropy rate D,,/n converges to zero at rate (logn)/n. The constant c, which we explicitly identify, depends only on the prior density function and the Fisher information matrix evaluated at the true parameter value. Consequences are given for density estimation, universal data compression, composite hypothesis testing, and stockmarket portfolio selection. 1.
An allornothing phenomenon for superefficiency
, 2008
"... In his 1953 paper Lucien Le Cam proved for regular univariate statistical models that sets of points of superefficiency have Lebesgue measure zero (in fact, these sets are even countable). Considering only computable estimators, it is possible to show that no computable parameter point can be a poin ..."
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In his 1953 paper Lucien Le Cam proved for regular univariate statistical models that sets of points of superefficiency have Lebesgue measure zero (in fact, these sets are even countable). Considering only computable estimators, it is possible to show that no computable parameter point can be a point of superefficiency. This strengthens Le Cam’s result to a dichotomy: either a parameter point θ can be computably estimated with zero error, or no computable estimator is more efficient at θ than the maximum likelihood estimator. 1