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Geometric ergodicity of the Gibbs sampler for Bayesian quantile regression

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  • Khare, Kshitij
  • Hobert, James P.

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.

Suggested Citation

  • Khare, Kshitij & Hobert, James P., 2012. "Geometric ergodicity of the Gibbs sampler for Bayesian quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 108-116.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:108-116
    DOI: 10.1016/j.jmva.2012.05.004
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    References listed on IDEAS

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    1. Bednorz, Witold & Latuszynski, Krzysztof, 2007. "A Few Remarks on," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1485-1486, December.
    2. Asmussen, Søren & Glynn, Peter W., 2011. "A new proof of convergence of MCMC via the ergodic theorem," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1482-1485, October.
    3. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    4. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
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