B-spline estimation for spatial data

Data collected on the surface of the earth often have spatial interaction. In this paper, a global smoothing procedure is developed using a tensor product of B-spline function approximations for estimating the spatial multi-dimensional conditional regression function. Under mild regularity assumptions, the global convergence rates of the B-spline estimators are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic normality of our estimator is also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations.