The reciprocal LASSO estimate for linear regression corresponds to a posterior mode when independent inverse Laplace priors are assigned on the regression coefficients. This paper studies reciprocal LASSO in quantile regression from a Bayesian perspective. Simple and efficient Gibbs sampling algorithms are developed for posterior inference using a scale mixture of inverse uniforms (or double Pareto densities), which can be further decomposed as a scale mixture of truncated normals. Slight modifications of this approach lead to Bayesian analogues of other related estimation methods, including reciprocal adaptive LASSO, reciprocal bridge, and reciprocal adaptive bridge. Empirical evidence of the attractiveness of the method is demonstrated via extensive simulation studies and two real data applications. Results show that the proposed methods perform quite well under a variety of scenarios.
