| Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models |
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| 引用本文： | GemaiChen Jin-hongYou. Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models[J]. 应用数学学报(英文版), 2005, 21(2): 177-192. DOI: 10.1007/s10255-005-0228-9 |
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| 作者姓名： | GemaiChen Jin-hongYou |
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| 作者单位： | [1]DepartmentofMathematicsandStatistics,UniversityofCalgary.Calgary,Alberta,CanadaT2N1N4 [2]DepartmentofBiostatistics,UniversityofNorthCarolina,ChapelHill,NC27599-7420,USA |
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| 基金项目： | supported by a grant from the Natural Sciences and Engineering Research Council of Canada. |
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| 摘 要： | Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.
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| 关 键 词： | 偏线性回归模型 异方差误差方差 迭代加权半参数最小平方误差 渐近正则 |
| 收稿时间： | 2004-04-10 |
Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models |
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| Gemai Chen,Jin-hong You. Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models[J]. Acta Mathematicae Applicatae Sinica, 2005, 21(2): 177-192. DOI: 10.1007/s10255-005-0228-9 |
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| Authors: | Gemai Chen Jin-hong You |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4;(2) Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7420, USA |
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| Abstract: | Abstract Consider a repeated measurement partially linear regression model with an unknown vector parameter β 1, an unknown function g(·), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions. The first author’s research is supported by a grant from the Natural Sciences and Engineering Research Council of Canada. |
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| Keywords: | Partially linear regression model heteroscedastic error variance iterative weighted semiparametric least squares estimator (IWSLSE) asymptotic normality |
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