Statistics Papers

Document Type

Journal Article

Date of this Version

5-15-2002

Publication Source

Statistics & Probability Letters

Volume

58

Issue

1

Start Page

23

Last Page

30

DOI

10.1016/S0167-7152(02)00097-4

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.

Copyright/Permission Statement

© 2002. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Keywords

nonparametric regression, point estimation, Bayesian procedure, Gaussian prior, optimum rate

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Date Posted: 27 November 2017

This document has been peer reviewed.