Bayesian composite $$L^p$$ -quantile regression

Abstract

\(L^p\) -quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles, \(p=1\) , and expectiles, \(p=2\) , as special cases. This paper studies composite \(L^p\) -quantile regression, simultaneously extending single \(L^p\) -quantile regression and composite quantile regression. A Bayesian approach is considered, where a novel parameterization of the skewed exponential power distribution is utilized. Further, a Laplace prior on the regression coefficients allows for variable selection. Through a Monte Carlo study and applications to empirical data, the proposed method is shown to outperform Bayesian composite quantile regression in most aspects.