B-spline estimation for semiparametric varying-coefficient partially linear regression with spatial data

Abstract

This paper considers a varying-coefficient partially linear regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the unknown parameters and coefficient functions. Under mild regularity assumptions, the asymptotic distribution of the estimator of the unknown parameter vector is established. The global convergence rates of the B-spline estimators of the unknown coefficient functions are established. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Boston housing data is used to illustrate our proposed methodology.