Simulation Study for Penalized Bayesian Elastic Net Quantile Regression

Bayesian regression analysis has great importance in recent years, especially in the Regularization method, Such as ridge, Lasso, adaptive lasso, elastic net methods, where choosing the prior distribution of the interested parameter is the main idea in the Bayesian regression analysis. By penalizing the Bayesian regression model, the variance of the estimators are reduced notable and the bias is getting smaller. The tradeoff between the bias and variance of the penalized Bayesian regression estimator consequently produce more interpretable model with more prediction accuracy. In this paper, we proposed new hierarchical model for the Bayesian quantile regression by employing the scale mixture of normals mixing with truncated gamma distribution that stated by (Li and Lin, 2010) as Laplace prior distribution. Therefore, new Gibbs sampling algorithms are introduced. A comparison has made with classical quantile regression model and with lasso quantile regression model by conducting simulations studies. Our model is comparable and gives better results.