Abstract
Abstract Bayesian nonparametric methods provide a natural setting for quantile regression, which offers great flexibility in assessing covariate effects on the response. In this paper, a method of estimating conditional quantile functions via Fourier series is proposed from a Bayesian perspective, which involves fewer smoothing parameter selection than that of spline-based quantile regression. Unlike most of existing Bayesian inference on quantile regression, the prior distributions are quantile dependent. The method can be implemented with Gibbs sampler based on a mixture representation of asymmetric Laplace distribution. The mean integrated squared error of the Bayes estimator can converge to 0 at different quantiles. Simulation studies and real data examples illustrate the practical utility of the procedure.
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