Geometric ergodicity of the Gibbs sampler for Bayesian quantile regression

Consider the quantile regression model Y = X beta + sigma is an element of where the components of is an element of are i.i.d. errors from the asymmetric Laplace distribution with rth quantile equal to 0, where r is an element of (0, 1) is fixed. Kozumi and Kobayashi (2011) [9] introduced a Gibbs sampler that can be used to explore the intractable posterior density that results when the quantile regression likelihood is combined with the usual normal/inverse gamma prior for (beta, sigma). In this paper, the Markov chain underlying Kozumi and Kobayashi's (2011) [9] algorithm is shown to converge at a geometric rate. No assumptions are made about the dimension of X, so the result still holds in the "large p, small n" case. (C) 2012 Elsevier Inc. All rights reserved.