New Bayesian Single Index Quantile Regression Based on Uniform Scale Mixture

Abstract

To scale back the dimensionality while holding a lot of flexibility of a nonparametric model Wu, et al. (2010) proposed a single index conditional quantile regression model. In this paper, a new Bayesian lasso for single index quantile regression model is proposed based on a scale mixture uniform. In addition, we construct an efficient and sampling  Gibbs algorithm for posterior inference based on a uniform scale mixture representation for Laplace distribution. Simulation study have considered to evaluate our proposed method compare to the existing methods. The results of simulations indicate that the new Bayesian algorithm performs well.