Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (5): 1113-1127.doi: 10.1016/S0252-9602(09)60090-4

• Articles •     Next Articles

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

Zhou Yong;You Jinhong;Wang Xiaojing    

  1. 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)

Abstract:

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.

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

CLC Number: 

  • 62G20
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