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

$$L^p$$ L p -quantiles are a class of generalized quantiles defined as minimizers of an asymmetric power function. They include both quantiles, $$p=1$$ p = 1 , and expectiles, $$p=2$$ p = 2 , as special cases. This paper studies composite $$L^p$$ L p -quantile regression, simultaneously extending single $$L^p$$ 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.