SPATIAL CONDITIONAL QUANTILE REGRESSION: WEAK CONSISTENCY OF A KERNEL ESTIMATE

摘要

We consider a conditional quantile regression model for spatial data. More precisely, given a strictly stationary random field Z_1 = (X_1, Y_1)_(i∈N~N), we investigate a kernel estimate of the conditional quantile regression function of the univariate response variable Y_1 given the functional variable X_i. The main purpose of the paper is to prove the convergence (with rate) in L~p norm and the asymptotic normality of the estimator.