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Gibbs Sampling Methods for Bayesian Quantile Regression

Author

Listed:
  • Hideo Kozumi

    (Graduate School of Business Administration, Kobe University)

  • Genya Kobayashi

    (Graduate School of Business Administration, Kobe University)

Abstract
This paper considers quantile regression models using an asymmetric Laplace distribution from a Bayesian point of view. We develop a simple and efficient Gibbs sampling algorithm for fitting the quantile regression model based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the resulting Gibbs sampler can be accomplished by sampling from either normal or generalized inverse Gaussian distribution. We also discuss some possible extensions of our approach, including the incorporation of a scale parameter, the use of double exponential prior, and a Bayesian analysis of Tobit quantile regression. The proposed methods are illustrated by both simulated and real data.

Suggested Citation

  • Hideo Kozumi & Genya Kobayashi, 2009. "Gibbs Sampling Methods for Bayesian Quantile Regression," Discussion Papers 2009-02, Kobe University, Graduate School of Business Administration.
    • Handle: RePEc:kbb:dpaper:2009-02
    as

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    File URL: https://www.b.kobe-u.ac.jp/papers_files/2009_02.pdf
    File Function: First version, 2009
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    References listed on IDEAS

    as
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