QUANTILE REGRESSION FOR SPATIALLY CORRELATED DATA: AN EMPIRICAL LIKELIHOOD APPROACH

Quantile regression is a useful approach to modeling various aspects of conditional distributions. The Bayesian approach provides a natural framework for incorporating spatial correlation in a quantile regression model. This paper considers Bayesian spatial quantile regression using empirical likelihood as a working likelihood. The proposed approach inherits the merits of quantile regression in the sense that we can work with linear conditional quantile functions without having to assume a parametric form of the conditional distributions, and we allow each covariate to have differential impacts on different parts of the conditional distributions. Put into a Bayesian framework, this approach can incorporate spatial priors to smooth the conditional quantile functions across locations and across quantiles. We demonstrate both theoretically and empirically how the proposed approach can take advantage of spatial correlation to improve efficiency over the usual quantile regression estimators. An application to the statistical downscaling of daily precipitation in the Chicago area is given to illustrate the merit of our approach.