变系数模型变窗宽局部M-估计的相合性  

THE CONSISTENCE OF VARIABLE BANDWIDTH LOCAL M-ESTIMATION OF VARYING COEFFICIENT MODELS

作　　者：吴小腊[1,2] 李泽华[3] 刘万荣[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081 [2]华南农业大学珠江学院,广州510900 [3]华南农业大学理学院统计系,广州510642

出　　处：《系统科学与数学》2009年第6期818-827,共10页Journal of Systems Science and Mathematical Sciences

基　　金：湖南省自然科学基金(08jj6039)项目资助;国家自然科学基金(10871072)项目资助。

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.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. 

分 类 号：O212.1[理学—概率论与数理统计] O212.7[理学—数学]