Flexible Bayesian quantile regression based on the generalized asymmetric Huberised-type distribution

To enhance the robustness and flexibility of Bayesian quantile regression models using the asymmetric Laplace or asymmetric Huberised-type (AH) distribution, which lacks changeable mode, diminishing influence of outliers, and asymmetry under median regression, we propose a new generalized AH distribution which is achieved through a hierarchical mixture representation, thus leading to a flexible Bayesian Huberised quantile regression framework. With many parameters in the model, we develop an efficient Markov chain Monte Carlo procedure based on the Metropolis-within-Gibbs sampling algorithm. The robustness and flexibility of the new distribution are examined through intensive simulation studies and application to two real data sets.