BAYESIAN BOOTSTRAP OF THE QUANTILE REGRESSION ESTIMATOR - A LARGE-SAMPLE STUDY

The large sample property of the Bayesian bootstrap distribution of th e quantile regression estimator is investigated. When the pair of depe ndent and independent variables are resampled, the Bayesian bootstrap is shown to converge weakly in probability to the limiting distributio n of the quantile regression estimator. The Bayesian bootstrap thus ha s the same asymptotic distribution as the Frequentist bootstrap. In ad dition, the median of the Bayesian bootstrap distribution has the same asymptotic distribution as the quantile regression estimator.