Electronic Journal of Statistics

Regression in random design and Bayesian warped wavelets estimators

Thanh Mai Pham Ngoc

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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

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

First available in Project Euclid: 16 November 2009

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Zentralblatt MATH identifier

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

Nonparametric regression random design warped wavelets Bayesian methods


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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