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.

Keywords:

• spatial data
• varying-coefficient partially linear regression
• B-spline estimators
• convergence rate
• asymptotic distribution

Acknowledgements

The author thank both anonymous referees and an associate editor for their valuable comments and suggestions which improved the early version of this paper. This research was supported by the National Science Foundation of China (Grant No. 11071120).