Bayesian Quantile Regression for Partially Linear Additive Models

TL;DR

This paper introduces a Bayesian method for partially linear additive models in quantile regression, enabling automatic separation of nonlinear, linear, and zero components without pre-specification, using spike-and-slab priors and a Gibbs sampler.

Contribution

It develops a novel semiparametric Bayesian estimation technique with automatic model component selection for quantile regression.

Findings

Effective separation of model components demonstrated in simulations

Method successfully applied to real datasets

Gibbs sampler provides efficient posterior inference

Abstract

In this article, we develop a semiparametric Bayesian estimation and model selection approach for partially linear additive models in conditional quantile regression. The asymmetric Laplace distribution provides a mechanism for Bayesian inferences of quantile regression models based on the check loss. The advantage of this new method is that nonlinear, linear and zero function components can be separated automatically and simultaneously during model fitting without the need of pre-specification or parameter tuning. This is achieved by spike-and-slab priors using two sets of indicator variables. For posterior inferences, we design an effective partially collapsed Gibbs sampler. Simulation studies are used to illustrate our algorithm. The proposed approach is further illustrated by applications to two real data sets.