Bayesian composite Lp-quantile regression

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.