Employing the Bayesian Elastic Net in Quantile Regression with an
Application
Muntadher Hashim Mnati Almusaedi 1 Dr. Ahmad Naeem Flaih 2
stat.post32@qu.edu.iq ahmad.flaih@qu.edu.iq
University of Al-Qadisiyah
Corresponding Author: Muntadher Hashim Mnati Almusaedi 1 Emai stat.post32@qu.edu.iq
Corresponding Author: : Dr. Ahmad Naeem Flaih 2 Email: ahmad.flaih@qu.edu.iq
Abstract
In this paper we employing the Bayesian elastic net method in quantile regression. The two penalizing (ridge and
lasso) function usually combined to produce the elastic net method, in which the variance of the estimators are
reduced and the bias approaches the smaller value. The tradeoff between the bias and variance of the estimator
produced an interpretable regression model and gives more prediction accuracy. In this paper, we proposed new
Bayesian hierarchical model for the quantile regression by utilizing the scale mixture of normal mixing with
truncated gamma distribution (1,∞) which proposed by (Li and Lin, 2010) as Laplace prior distribution for the
parameter (β). Moreover, Gibbs sampling algorithms are introduced for the posterior distributions. Real data
application for the proposed model has been deducted and a comparison has been made with classical quantile
regression model, also with lasso quantile regression model .Our model is comparable and gives better results.
Keywords: Bayesian analysis, quantile regression, elastic net, Gibbs sampler
