Estimation and Variable Selection in Partially Linear Wavelet Models via Gibbs Sampling

• Activity Number: 302
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Norbert Remenyi*+
• Companies: Georgia Institute of Technology
• Keywords: Partially linear model ; Wavelet estimation ; Hierarchical model ; Bayesian estimation ; Gibbs sampling

Abstract

In this paper we propose a wavelet-based methodology for simultaneous 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 of wide ranges 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 linear and nonlinear part of the model we are using point-mass-at-zero contamination priors with double exponential spread distribution.

There has been only a few papers in the area of partially linear wavelet models, and we show that the proposed methodology is often superior to the existing methods in estimating parameters of the model. Moreover, the method is able to perform Bayesian variable selection by a stochastic search for the linear part of the model.

Applications of the model on simulated data are provided and comparisons with existing methods are made.