Bayesian Variable Selection In Quantile Regression

Since the seminal work of Koenker&Bassett[1](1978), quantile regression isgradually emerging as a comprehensive approach to the statistical analysis of linearand nonlinear response models. Compared with the mean regression, quantile re-gression can provide a more complete picture for the distribution. In practice, if thepredictor vector contains many variables, then it is necessary to select the signif-cant ones in order to improve the precision of the estimator. In this paper, based onthe stochastic search variable selection approach, we develop a simple and efcientGibbs sampling algorithm for Bayesian model selection in quantile regression basedon a location-scale mixture representation of the asymmetric laplace distribution.Also, we extended the approach in binary and tobit quantile regression. More-over, we consider variable selection in the single-index quantile regression modelbased on the stochastic search variable selection approach, where the link functionis modeled by trucated linear splines, and the distribution of the error is mod-eled nonparametrically by a Dirichlet process mixture model. Posterior inferenceis implemented using the Gibbs sampling and Metropolis-Hastings algorithm. Theabove models are illustrated using a large number of simulations. The results showthat our methods can efectively choose the true model. At last we analysis severalreal data examples.