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STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS |
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| Authors: | Zhou Yong You Jinhong Wang Xiaojing |
| Institution: | aAcademy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100190, China;bDepartment of Statistics, Shanghai University of Finance and Economics, Shanghai 200433, China;cDepartment of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA |
| 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. |
| Keywords: | partially linear regression model varying-coefficient profile leastsquares error variance strong convergence rate law of iterated logarithm2000 MR Subject Classification: 62G20 62G05 |
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