Geometric ergodicity of the Gibbs sampler for Bayesian quantile regression

Kshitij Khare and James P. Hobert

Journal of Multivariate Analysis, 2012, vol. 112, issue C, 108-116

Abstract: Consider the quantile regression model Y=Xβ+σϵ where the components of ϵ are i.i.d. errors from the asymmetric Laplace distribution with rth quantile equal to 0, where r∈(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 (β,σ). 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.

Keywords: Convergence rate; Geometric drift condition; Markov chain; Monte Carlo (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (17)

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DOI: 10.1016/j.jmva.2012.05.004

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