154 Hurley Hall
Bayesian High-Dimensional Quantile Regression
We consider a Bayesian high-dimensional quantile regression problem with diverging number of predictors or covariates. The error distribution of the observations is assumed to be an asymmetric Laplace distribution which may be different from the true error distribution. Sparse priors such as spike and slab type of priors are imposed on the coefficients of the covariates and inference is based on the posterior distribution. We obtain posterior contraction rate as well as prove a Bernstein-von Mises theorem for the posterior distribution of the coefficents.