部分线性回归模型变窗宽一步局部M-估计  

Variable Bandwidth One-step Local M-estimators of Partial Linear Models

作　　者：姚丽丽[1] 宋向东[1] 赵梦琳[1] 张云霞[1,2] 刘燕[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]河北科技师范学院欧美学院,河北秦皇岛066004

出　　处：《数学的实践与认识》2011年第22期167-173,共7页Mathematics in Practice and Theory

基　　金：秦皇岛市科学技术研究与发展计划(201101B025)

摘　　要：讨论了部分线性回归模型的变窗宽一步局部M-估计.用一步局部M-估计给出未知函数的估计,用平均方法给出参数估计.进一步通过两个引理证明一步M-估计的渐近正态性.所提出的方法继承了局部多项式的优点并且克服了最小二乘法缺乏稳健性的缺点.In the paper the variable bandwidth one-step local M-estimates of the un- known function and the unknown parameter of the partial linear models are discilssed. The estimators of parametric component on partial linear models are developed by one-step M- estimation method and average method , the estimators of nonparametric component are given by one-step M-estimation. Asymptotic properties of one-step M-estimators are proofed by two lemmas. The proposed method inherits the advantages of local polynomial regression and overcomes lack of robustness of least squares techniques.

关 键 词：部分线性回归模型 变窗宽 一步局部M-估计 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]