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

doi:10.1016/S0252-9602(09)60090-4

数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1113-1127.doi: 10.1016/S0252-9602(09)60090-4

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

周勇, 尤进红, 王晓婧

1.Academy of Mathematics and Systems Science, |Chinese Academy of Science, Beijing 100190, |China；2.Department of Statistics, Shanghai University of Finance and Economics, |Shanghai 200433, China；3.Department of Biostatistics,University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

收稿日期:2006-12-29 修回日期:2008-09-10 出版日期:2009-09-20 发布日期:2009-09-20
基金资助:
Zhou's research was supported by the National Natural Science Funds for Distinguished Young Scholar (70825004) and National Natural Science Foundation of China (NSFC) (10731010 and 10628104), the National Basic Research Program (2007CB814902), Creative Research Groups of China (10721101) and Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics and 211 Project for Shanghai University of Finance and Economics (the 3rd phase)

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

Zhou Yong；You Jinhong；Wang Xiaojing

1.Academy of Mathematics and Systems Science, |Chinese Academy of Science, Beijing 100190, |China；2.Department of Statistics, Shanghai University of Finance and Economics, |Shanghai 200433, China；3.Department of Biostatistics,University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Received:2006-12-29 Revised:2008-09-10 Online:2009-09-20 Published:2009-09-20
Supported by:
Zhou's research was supported by the National Natural Science Funds for Distinguished Young Scholar (70825004) and National Natural Science Foundation of China (NSFC) (10731010 and 10628104), the National Basic Research Program (2007CB814902), Creative Research Groups of China (10721101) and Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics and 211 Project for Shanghai University of Finance and Economics (the 3rd phase)

摘要/Abstract

摘要：

This article is concerned with the estimating problem of semiparametric varying-coefficient 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

Abstract:

Key words: partially linear regression model, varying coefficient, profile leastsquares, error variance, strong convergence rate, law of iterated logarithm

中图分类号:

62G20

周勇, 尤进红, 王晓婧. STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS[J]. 数学物理学报(英文版), 2009, 29(5): 1113-1127.

Zhou Yong；You Jinhong；Wang Xiaojing. STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS[J]. Acta mathematica scientia,Series B, 2009, 29(5): 1113-1127.

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

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

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