Fully Bayesian Estimation and Variable Selection in Partially Linear Wavelet Models

TL;DR

This paper introduces a Bayesian wavelet-based approach for estimating and selecting variables in partially linear models, effectively handling nonparametric components with varying smoothness.

Contribution

It presents a novel hierarchical Bayesian method using wavelet domain inference and point-mass priors for estimation and variable selection in partially linear models.

Findings

Method outperforms existing approaches in parameter estimation.

Enables Bayesian variable selection via stochastic search.

Effective for nonparametric components with different smoothness levels.

Abstract

In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for nonparametric components with various degrees of smoothness. A hierarchical Bayes model is formulated on the parameters of this representation, where the estimation and variable selection is performed by a Gibbs sampling procedure. For both the parametric and nonparametric part of the model we are using point-mass-at-zero contamination priors with a double exponential spread distribution. Only a few papers in the area of partially linear wavelet models exist, and we show that the proposed methodology is often superior to the existing methods with respect to the task of estimating model parameters. Moreover, the method is able to perform Bayesian variable selection by a stochastic search for the parametric part of the model.