Bayesian quantile regression for semiparametric models

Abstract

Quantile regression has recently received a great deal of attention in both theoretical and empirical research. It can uncover different structural relationships between covariates and responses at the upper or lower tails, which is sometimes of significant interest in econometrics, educational and medicine applications. The methodologies of quantile regression for linear models have been well developed in both frequentist and Bayesian contexts. However, there has been relatively less work focusing on quantile regression for nonparametric models or semiparametric models, especially from a Bayesian perspective.

The principal goal of this work is to propose efficient approaches to implement Bayesian quantile regression with two kinds of semiparametric modes, single-index models and partially linear additive models, using an asymmetric Laplace distribution which provides a mechanism for Bayesian inference of quantile regression. With carefully selected priors, we build hierarchical Bayesian models and design effective Markov chain Monte Carlo algorithms for posterior inference. We compare the proposed methods with some existing methods through simulation studies and real data applications.