Electronic Journal of Statistics

Regression in random design and Bayesian warped wavelets estimators

Thanh Mai Pham Ngoc

Full-text: Open access

Abstract

In this paper we deal with the regression problem in a random design setting. We investigate asymptotic optimality under minimax point of view of various Bayesian rules based on warped wavelets. We show that they nearly attain optimal minimax rates of convergence over the Besov smoothness class considered. Warped wavelets have been introduced recently, they offer very good computable and easy-to-implement properties while being well adapted to the statistical problem at hand. We particularly put emphasis on Bayesian rules leaning on small and large variance Gaussian priors and discuss their simulation performances, comparing them with a hard thresholding procedure.

Article information

Source
Electron. J. Statist., Volume 3 (2009), 1084-1112.

Dates
First available in Project Euclid: 16 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1258380624

Digital Object Identifier
doi:10.1214/09-EJS466

Mathematical Reviews number (MathSciNet)
MR2566182

Zentralblatt MATH identifier
1326.62077

Subjects
Primary: 62G05: Estimation 62G08: Nonparametric regression 62G20: Asymptotic properties 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Nonparametric regression random design warped wavelets Bayesian methods

Citation

Pham Ngoc, Thanh Mai. Regression in random design and Bayesian warped wavelets estimators. Electron. J. Statist. 3 (2009), 1084--1112. doi:10.1214/09-EJS466. https://projecteuclid.org/euclid.ejs/1258380624


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