B-spline estimation for varying coefficient regression with spatial data  

作　　者：TANG QingGuo CHENG LongSheng 

机构地区：[1]School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China [2]Institute of Sciences,PLA University of Science and Technology,Nanjing 210007,China

出　　处：《Science China Mathematics》2009年第11期2321-2340,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No. 10671089);China Postdoctoral Science Foundation and Jiangsu Planned Projects for Postdoctoral Research Funds

摘　　要：This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions, the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election.

关 键 词：spatial data varying coefficient regression B-spline estimators convergence rate asymptotic distribution 62G05 62G08 

分 类 号：O212.1[理学—概率论与数理统计]