Bayesian Lasso and adaptive Lasso expectile regression

This article considers regularization in expectile regression from a Bayesian framework. Specifically, we proposed two Bayesian regularization approaches for covariate selection and estimation in expectile regression: the Bayesian Lasso and adaptive Lasso expectile regression. Two simple and efficient Gibbs sampling algorithms were developed for posterior inference using a scale mixture of uniform (SMU) representation of the Laplace density. The proposed approaches are illustrated via simulation studies and two real data sets. Compared to some of the existing approaches, results show that the proposed approaches perform very well under a variety of simulation studies and the real data sets.