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Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

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Acta Mathematicae Applicatae Sinica 2005年第2期21卷 177-192页

作者： gemaichen Jin-hongYou DepartmentofMathematicsandStatistics UniversityofCalgary.CalgaryAlbertaCanadaT2N1N4 DepartmentofBiostatistics UniversityofNorthCarolinaChapelHillNC27599-7420USA

Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.

关键词： Partially linear regression model heteroscedastic error variance iterativeweighted semiparametric least squares estimator (IWSLSE) asymptotic normality

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Uniform Convergence Rate of Estimators of Autocovariances in Partly Linear Regression Models with Correlated Errors

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Acta Mathematicae Applicatae Sinica 2003年第3期19卷 363-370页

作者： Jin-hongYou gemaichen MinChen ue-leiJiang UniversityofRegina ReginaSaskatchewanS4S0A2Canada UniversityofCalgary CalgaryAlbertaT2N1N4Canada AcademyofMathematicsandSystemSciences ChineseAcademyofSciencesBeijing100080.China

Consider the partly linear regression model , where y i ’s are responses, are known and nonrandom design points, is a compact set in the real line , β = (β 1, ··· , β p )' is an unknown parameter vector, g(·) is an unknown function and {ε i } is a linear process, i.e., , where e j are i.i.d. random variables with zero mean and variance . Drawing upon B-spline estimation of g(·) and least squares estimation of β, we construct estimators of the autocovariances of {ε i }. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {ε i } are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process.

关键词： Uniform strong convergence rate autocovariance and autocorrelation B-spline estimation correlated error partly linear regression model

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ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

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Journal of Systems Science & Complexity 2004年第4期17卷 511-522页

作者： JinhongYOU CHENMin gemaichen UniversityofRegina ReginaSaskatchewanS4S0A2Canada AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080China UniversityofCalgary CalgaryAlbertaT2N1N4Canada

Consider a semiparametric regression model with linear time series errors Y_k= x′ _kβ + g(t_k) + ε_k, 1 ≤ k ≤ n, where Y_k's are responses, x_k =(x_(k1),x_(k2),···,x_(kp))′ and t_k ∈ T is contained in R are fixed design points, β =(β_1,β_2,···,β_p)′ is an unknown parameter vector, g(·) is an unknown bounded real-valuedfunction defined on a compact subset T of the real line R, and ε_k is a linear process given byε_k = ∑ from j=0 to ∞ of ψ_je_(k-j), ψ_0=1, where ∑ from j=0 to ∞ of |ψ_j| < ∞, and e_j,j=0, +-1, +-2,···, ard i.i.d. random variables. In this paper we establish the asymptoticnormality of the least squares estimator of β, a smooth estimator of g(·), and estimators of theautocovariance and autocorrelation functions of the linear process ε_k.

关键词： semiparametric regression model fixed-design asymptotic normality lineartime series errors

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