## The Annals of Statistics

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

Marianna Pensky

#### 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.

#### Article information

Source
Ann. Statist., Volume 34, Number 2 (2006), 769-807.

Dates
First available in Project Euclid: 27 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1151418240

Digital Object Identifier
doi:10.1214/009053606000000128

Mathematical Reviews number (MathSciNet)
MR2283392

Zentralblatt MATH identifier
1095.62049

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

#### Citation

Pensky, Marianna. Frequentist optimality of Bayesian wavelet shrinkage rules for Gaussian and non-Gaussian noise. Ann. Statist. 34 (2006), no. 2, 769--807. doi:10.1214/009053606000000128. https://projecteuclid.org/euclid.aos/1151418240

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