This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural semiparametric way. The local M-estimators of the unknown functional-coefficient functions are proposed by using local linear approximation, and their asymptotic distributions are then established under weak spatial mixing conditions allowing the data processes to be either stationary or nonstationary with spatial trends. Application to a soil data set is demonstrated with interesting findings that go beyond traditional analysis.
"Estimating spatial quantile regression with functional coefficients: A robust semiparametric framework." Bernoulli 20 (1) 164 - 189, February 2014. https://doi.org/10.3150/12-BEJ480