Title

Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise

Authors

Authors

M. Pensky

Comments

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Abbreviated Journal Title

Ann. Stat.

Keywords

bayesian models; optimality; Sobolev and Besov spaces; nonparametric; regression; wavelet shrinkage; SELECTION; Statistics & Probability

Abstract

The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in a nonparametric regression model with i.i.d. errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish a relationship between hyperparameters, verify that the majority of Bayesian models studied so far achieve theoretical optimality, state which Bayesian models cannot achieve optimal convergence rate and explain why it happens.

Journal Title

Annals of Statistics

Volume

34

Issue/Number

2

Publication Date

1-1-2006

Document Type

Article

Language

English

First Page

769

Last Page

807

WOS Identifier

WOS:000238884500007

ISSN

0090-5364

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