Bayesian Lasso Quantile Regression. The method extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coefficients. In particular we propose a new Bayesian Lasso method that employs a skewed Laplace distribution for the errors and a scaled mixture of uniform distribution for the regression parameters together with Bayesian MCMC estimation.
Abstract - Add to MetaCart. Simple and efficient Gibbs sampling algorithms are developed for posterior inference using a scale mixture. The penalized linear mixed quantile regression Our approach is to set up the problem as a Bayesian quantile regression problem under the l1 penalty.
Min Xn i1 ˆ py i gx0 i k k 1.
Existing approaches to variable selection in a binary classification context are sensitive to outliers heteroskedasticity or other anomalies of the latent response. The method extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coefficients. The proposed method is demonstrated via simulation studies and a real data set. The asymmetric Laplace error distribution is written as a scale mixture of normals as in Reed and Yu 2009.
