Generalized Profile LSE in Varying-Coefficient Partially Linear Models with Measurement Errors  

作　　者：Yun-bei MA Jin-hong YOU Yong ZHOU 

机构地区：[1]School of Statistics,Southwestern University of Finance and Economics [2]School of Statistics and Management,Shanghai University of Finance and Economics [3]Academy of Mathematics and System Sciences,Chinese Academy of Sciences

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第3期477-490,共14页应用数学学报（英文版）

基　　金：supported by National Natural Science Funds for Distinguished Young Scholar(No.70825004) and (No.71271128);Creative Research Groups of China(No.71271128);NCMIS and Shanghai University of Finance and Economics through Project 211 Phase Ⅲ;Shanghai Leading Academic Discipline Project(No.B803)

摘　　要：This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ＋Zτiα（Ui）＋εi , Wi=Xi＋ξi,i=1, · · · , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ＋Zτiα（Ui）＋εi , Wi=Xi＋ξi,i=1, · · · , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.

关 键 词：Semiparametric modeling varying-coefficient measurement error local polynomial profile least squares asymptotic normality 

分 类 号：O212.1[理学—概率论与数理统计] O175.1[理学—数学]