Bayesian Nonparametric Point Estimation Under a Conjugate Prior
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Statistics Papers
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nonparametric regression
point estimation
Bayesian procedure
Gaussian prior
optimum rate
Statistics and Probability
point estimation
Bayesian procedure
Gaussian prior
optimum rate
Statistics and Probability
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Li, Xuefeng
Zhao, Linda H
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Abstract
Estimation of a nonparametric regression function at a point is considered. The function is assumed to lie in a Sobolev space, Sq, of order q. The asymptotic squared-error performance of Bayes estimators corresponding to Gaussian priors is investigated as the sample size, n, increases. It is shown that for any such fixed prior on Sq the Bayes procedures do not attain the optimal minimax rate over balls in Sq. This result complements that in Zhao (Ann. Statist. 28 (2000) 532) for estimating the entire regression function, but the proof is rather different.
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2002-05-15
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Statistics & Probability Letters