Traditional Bayesian quantile regre

Traditional Bayesian quantile regression relies on the Asymmetric Laplace (AL)distribution due primarily to its satisfactory empirical and theoretical performances. However, the AL displays medium tails and it is not suitable for datacharacterized by strong deviations from the Gaussian hypothesis. An extensionof the AL Bayesian quantile regression framework is proposed to account for fattails using the Skew Exponential Power (SEP) distribution. Linear and AdditiveModels (AM) with penalized splines are considered to show the flexibility of theSEP in the Bayesian quantile regression context. Lasso priors are used in bothcases to account for the problem of shrinking parameters when the parametersspace becomes wide while Bayesian inference is implemented using a new adaptive Metropolis within Gibbs algorithm. Empirical evidence of the statisticalproperties of the proposed models is provided through several examples basedon both simulated and real datasets.