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April 2006 Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise
Marianna Pensky
Ann. Statist. 34(2): 769-807 (April 2006). DOI: 10.1214/009053606000000128

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.

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Marianna Pensky. "Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise." Ann. Statist. 34 (2) 769 - 807, April 2006. https://doi.org/10.1214/009053606000000128

Information

Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1095.62049
MathSciNet: MR2283392
Digital Object Identifier: 10.1214/009053606000000128

Subjects:
Primary: 62G08
Secondary: 62C10

Keywords: Bayesian models , Nonparametric regression , optimality , Sobolev and Besov spaces , wavelet shrinkage

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 2 • April 2006
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