变系数模型变窗宽局部M-估计的相合性

吴小腊;李泽华;刘万荣

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 818-827.

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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 818-827. DOI: 10.12341/jssms08422
论文

变系数模型变窗宽局部M-估计的相合性

    吴小腊(1), 李泽华(2), 刘万荣(3)
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The Consistence of Variable Bandwidth Local M-Estimation of Varying Coefficient Models

    WU Xiaola(1), LI Zehua(2), LIU Wanrong
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摘要

用变窗宽局部M-估计对变系数模型的系数函数进行估计,得到了估计的相合性和渐近正态性.所采用的方法继承了局部多项式回归的优点并且克服了最小二乘方法缺乏稳健性的缺点.变窗宽的使用提高了局部M-估计的可塑性,并使得它们能成功地处理空间非齐性曲线、异方差性及非均匀设计密度.

Abstract

In this paper, the variable bandwidth local M approach is employed to estimate the coefficient functions in varying coefficient models, and the consistence and the asymptotical normality of the robust M-estimation is given. The proposed method inherits the advantages of local polynomial regression and overcomes lack of robustness of least squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and make them possible to cope well with spatially inhomogeneous curve, heteroscedasticity and nonuniform design density.

关键词

变系数模型 / 局部M-估计 / 变窗宽.

Key words

Varying coefficient models / local M-estimation / variable bandwidth.

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吴小腊 , 李泽华 , 刘万荣. 变系数模型变窗宽局部M-估计的相合性. 系统科学与数学, 2009, 29(6): 818-827. https://doi.org/10.12341/jssms08422
WU Xiaola , LI Zehua , LIU Wanrong. The Consistence of Variable Bandwidth Local M-Estimation of Varying Coefficient Models. Journal of Systems Science and Mathematical Sciences, 2009, 29(6): 818-827 https://doi.org/10.12341/jssms08422
中图分类号： 62G05   
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