变系数模型变窗宽局部M-估计的渐近正态性  

Variable Bandwidth and Local M-estimation of Varying Coefficient Models

作　　者：吴小腊[1] 刘万荣[1] 李泽华[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

出　　处：《重庆师范大学学报（自然科学版）》2008年第1期50-53,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.30230210)

摘　　要：局部多项式回归方法已证明是一个有效的非参数回归方法,有优于流行核方法的特点,如设计的自适应性和高的渐进效率。然而,它的一个缺点是缺乏稳健性。M-型估计是达到所需稳健性的一种自然预期。而且常窗宽对齐次待估曲线是合理的,但对更复杂的曲线如非齐次的,异方差的曲线则失去灵活性,为了完全做到用模型数据去估计参数,本文结合上述两种方法,对变系数模型的系数参数进行估计,并在其中嵌入一个变窗宽加以提高,得到了估计的渐进正态性。Local polynomial regression methods have been demonstrated as effective nonparametric smoothers. They have advantages over popular kernel methods, in terms of the ability of design adaptation and high asymptotic efficiency. Moreover, the local polynomial regression smoothers can adapt to almost all regression settings and cope very well with the edge effects. A drawback of these local re- gression estimators is, however , lack of robustness, and M-type of regression estimators are natural candidates for achieving desirable robustness properties. In this paper the variable bandwidth and one step local M approach is employed to estimate the coefficient functions in varying coefficient models. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming in lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of resulting local M-estimators and makes them possihle to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exit arid are asymptotically normal. This paper focus on establishing joint asymptotic normality of the nonparametric M-type estimators of coefficient functions and its associated derivaion based on local linear regression smoothers implemented with variable bandwidth.

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]