Bayesian Nonparametric Modeling in Quantile Regression

We propose Bayesian nonparametric methodology for quantile regression modeling. In particular, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed nonparametric prior probability models allow the data to drive the shape of the error density and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models which allow the error distribution to change nonparametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets.