| Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs |
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| 引用本文： | Xing-weiTong Heng-jianCui HuiZhao. Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs[J]. 应用数学学报(英文版), 2005, 21(2): 257-268. DOI: 10.1007/s10255-005-0234-y |
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| 作者姓名： | Xing-weiTong Heng-jianCui HuiZhao |
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| 作者单位： | Xing-wei Tong~1，Heng-jian Cui~2，Hui Zhao~3 1，2 Department of Mathematics，Beijing Normal University，Beijing 100875，China 3 Department of Statistics，Central China Normal University，Wuhan 430079，China |
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| 基金项目： | Supported by The National Natural Science Foundation of China (No. 10231030 )，Beijing Normal University Youth Foundation (No. 104951). |
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| 摘 要： | For partial linear model Y=X~τβ_0 _(g0)(T) εwith unknown β_0∈R~d and an unknown smooth function go, this paper considers the Huber-Dutter estimators of β_0, scale σfor the errors and the function go respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σare asymptotically normal with convergence rate n~((-1)/2) and the B-spline Huber-Dutter estimator of go achieves the optimal convergence rate in nonparametric regression. A simulation study demonstrates that the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study.
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| 关 键 词： | 胡布尔-达特稳健估计 偏线性模型 优化收敛率 β-样条函数 |
| 收稿时间： | 2004-05-05 |
Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs |
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| Xing-wei Tong,Heng-jian Cui,Hui Zhao. Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs[J]. Acta Mathematicae Applicatae Sinica, 2005, 21(2): 257-268. DOI: 10.1007/s10255-005-0234-y |
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| Authors: | Xing-wei Tong Heng-jian Cui Hui Zhao |
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| Affiliation: | (1) Department of Mathematics, Beijing Normal University, Beijing 100875, China;(2) Department of Statistics, Central China Normal University, Wuhan 430079, China |
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| Abstract: | Abstract For partial linear model Y = X τ β 0 + g 0(T) + ε with unknown β 0 ∈? R d and an unknown smooth function g 0, this paper considers the Huber-Dutter estimators of β 0, scale σ for the errors and the function g 0 respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β 0 and σ are asymptotically normal with convergence rate n -1/2 and the B-spline Huber-Dutter estimator of g 0 achieves the optimal convergence rate in nonparametric regression. A simulation study demonstrates that the Huber-Dutter estimator of β 0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study. Supported by The National Natural Science Foundation of China (No. 10231030 ) and Beijing Normal University Youth Foundation ( No. 104951). |
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| Keywords: | Huber-dutter estimator partial linear model m-estimator optimal convergence rate B-spline function |
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