Authors

M. Pensky;T. Sapatinas

Comments

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Abbreviated Journal Title

Stat. Sin.

Keywords

bayesian inference; Besov spaces; empirical Bayes inference; nonparametric regression; optimality; wavelets; SPARSE SEQUENCES; SHRINKAGE; SELECTION; RULES; Statistics & Probability

Abstract

We investigate the theoretical performance of Bayes factor estimators in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We compare these estimators in terms of their frequentist optimality in Besov spaces for a wide variety of error and prior distributions. Furthermore, we provide sufficient conditions that determine whether the underlying regression function belongs to a Besov space a-priori with probability one. We also study an adaptive estimator by considering an empirical Bayes estimation procedure of the Bayes factor estimator for a certain combination of error and prior distributions. Simulated examples are used to illustrate the performance of the empirical Bayes estimation procedure based on the proposed Bayes factor estimator, and compared with two recently proposed empirical Bayes estimators. An application to a dataset that was collected in ail anaesthesiological study is also presented.

Journal Title

Statistica Sinica

Volume

17

Issue/Number

2

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

599

Last Page

633

WOS Identifier

WOS:000249307200012

ISSN

1017-0405

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