Regression in random design and Bayesian warped wavelets estimators

TL;DR

This paper investigates Bayesian warped wavelet estimators for regression in a random design setting, demonstrating their near-optimal convergence rates and comparing their performance with traditional thresholding methods.

Contribution

It introduces Bayesian warped wavelet rules for regression, showing they nearly achieve minimax optimality and are computationally feasible in a random design context.

Findings

Bayesian warped wavelet estimators nearly attain minimax convergence rates.

They are computationally simple and well-adapted to the statistical problem.

Simulation results favor Bayesian rules over hard thresholding.

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 and 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.