The Expectation-Maximization approach for Bayesian quantile regression

This paper deals with Bayesian linear quantile regression models based on a recently developed Expectation-Maximization Variable Selection (EMVS) method. By using additional latent variables, the proposed approach enjoys enormous computational savings compared to commonly used Markov Chain Monte Carlo (MCMC) algorithm. Using location-scale mixture representation of asymmetric Laplace distribution (ALD), we develop a rapid and efficient Expectation-Maximization (EM) algorithm, which is illustrated with several carefully designed simulation examples. We further apply the proposed method to construct financial index tracking portfolios.