STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS  

作　　者：周勇 尤进红 王晓婧 

机构地区：[1]Academy of Mathematics and Systems Science, Chinese Academy of Science [2]Department of Statistics, Shanghai University of Finance and Economics [3]Department of Biostatistics,University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

出　　处：《Acta Mathematica Scientia》2009年第5期1113-1127,共15页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Funds for Distinguished Young Scholar (70825004);National Natural Science Foundation of China (NSFC) (10731010 and 10628104);the National Basic Research Program (2007CB814902);Creative Research Groups of China (10721101);Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics;211 Project for Shanghai University of Financeand Economics (the 3rd phase)

摘　　要：This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.

关 键 词：partially linear regression model varying-coefficient profile leastsquares error variance strong convergence rate law of iterated logarithm 

分 类 号：O212[理学—概率论与数理统计]