Efficiency of Bayesian Approaches in Quantile Regression with Small Sample Size

Quantile regression is a statistical technique intended to estimate, and conduct inference about the conditional quantile functions. Just as the classical linear regression methods estimate model for the conditional mean function, quantile regression offers a mechanism for estimating models for the conditional median function, and the full range of other conditional quantile functions. In the Bayesian approach to variable selection prior distributions representing the subjective beliefs about the parameters are assigned to the regression coefficients. The estimation of parameters and the selection of the best subset of variables is accomplished by using adaptive lasso quantile regression. In this paper we describe, compare, and apply the two suggested Bayesian approaches. The two suggested Bayesian suggested approaches are used to select the best subset of variables and estimate the parameters of the quantile regression equation when small sample sizes are used.  Simulations show that the proposed approaches are very competitive in terms of variable selection, estimation accuracy and efficient when small sample sizes are used.