Robust estimation for spatial semiparametric varying coefficient partially linear regression

This paper considers a varying coefficient partially linear regression with spatial data. A general formulation is used to treat mean regression, median regression, quantile regression and robust mean regression in one setting. The parametric estimators of the model are obtained through piecewise local polynomial approximation of the nonparametric coefficient functions. The local estimators of unknown coefficient functions are obtained by replacing the parameters in model with their estimators and using local linear approximations.The asymptotic distribution of the estimator of the unknown parameter vector is established. The asymptotic distributions of the estimators of the unknown coefficient functions at both interior and boundary points are also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about spatial soil data is used to illustrate our proposed methodology.