Alhamzawi, Yu, and Benoit 2012

Statistical Modelling 12 (2012), 279–297

Bayesian adaptive Lasso quantile regression

Rahim Alhamzawi
Department of Mathematics,
Brunel University
Uxbridge UB8 3PH
UK
eMail:

Keming Yu
Department of Mathematics,
Brunel University
Uxbridge UB8 3PH
UK

Dries F Benoit
Department of Marketing,
Faculty of Economics and Business Administration,
Ghent University
Ghent
Belgium

Abstract:

Recently, variable selection by penalized likelihood has attracted much research interest. In this paper, we propose adaptive Lasso quantile regression (BALQR) from a Bayesian perspective. The method extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coefficients. Inverse gamma prior distributions are placed on the penalty parameters. We treat the hyperparameters of the inverse gamma prior as unknowns and estimate them along with the other parameters. A Gibbs sampler is developed to simulate the parameters from the posterior distributions. Through simulation studies and analysis of a prostate cancer dataset, we compare the performance of the BALQR method proposed with six existing Bayesian and non-Bayesian methods. The simulation studies and the prostate cancer data analysis indicate that the BALQR method performs well in comparison to the other approaches.

Keywords:

Gibbs sampler; Lasso; quantile regression; skewed Laplace distribution

Downloads:

R-package including example data in zipped archive

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