Date of this Version
Statistics & Probability Letters
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.
© 2002. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.
nonparametric regression, point estimation, Bayesian procedure, Gaussian prior, optimum rate
Li, X., & Zhao, L. H. (2002). Bayesian Nonparametric Point Estimation Under a Conjugate Prior. Statistics & Probability Letters, 58 (1), 23-30. http://dx.doi.org/10.1016/S0167-7152(02)00097-4
Date Posted: 27 November 2017
This document has been peer reviewed.