Consistency and normality of Huber-Dutter estimators for partial linear model
Consistency and normality of Huber-Dutter estimators for partial linear model
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DOI：
10.1007/s11425-008-0028-9
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发表时间：
2008-09
期刊：
影响因子：
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通讯作者：
Xingwei Tong;H. Cui;P. Yu
中科院分区：
文献类型：
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作者：
Xingwei Tong;H. Cui;P. Yu
对于部分线性模型Y=Xτβ0+G0(T)+∈具有未知的β0∈ȑD和未知的光滑函数0，本文分别考虑了β0的估计、误差的尺度σ估计和光滑B样条函数逼近的函数0的Huber-duter估计。在一定的正则性条件下，证明了β0和σ的估计随−1/2的收敛速度是渐近正态的，且g0的B样条估计在非参数回归中达到了最优的收敛速度.仿真研究和两个例子表明，β0的Huber-duter估计与其无尺度参数的M-估计和普通的最小二乘估计是竞争的。
For partial linear modelY=Xτβ0+g0(T) +∈with unknownβ0∈ ȑdand an unknown smooth functiong0, this paper considers the Huber-Dutter estimators ofβ0, scaleσfor the errors and the functiong0approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators ofβ0andσare shown to be asymptotically normal with the rate of convergencen−1/2and the B-spline Huber-Dutter estimator ofg0achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator ofβ0is competitive with its M-estimator without scale parameter and the ordinary least square estimator.