  In this article, we develop a semiparametric Bayesian estimation and model
selection approach for partially linear additive models in conditional quantile
regression. The asymmetric Laplace distribution provides a mechanism for
Bayesian inferences of quantile regression models based on the check loss. The
advantage of this new method is that nonlinear, linear and zero function
components can be separated automatically and simultaneously during model
fitting without the need of pre-specification or parameter tuning. This is
achieved by spike-and-slab priors using two sets of indicator variables. For
posterior inferences, we design an effective partially collapsed Gibbs sampler.
Simulation studies are used to illustrate our algorithm. The proposed approach
is further illustrated by applications to two real data sets.
