部分线性模型的M-估计  

M-Estimation on Partially Linear Models

作　　者：魏娟[1] 吕士钦[1] 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2012年第1期73-76,共4页Journal of North University of China(Natural Science Edition)

基　　金：山西省软科学基金资助项目(2010041057-04)

摘　　要：部分线性模型已获得广泛的研究和应用,其未知参数和函数的估计方法往往不具有稳健性.研究了部分线性模型的稳健M-估计,用局部线性方法和平均方法给出了常系数的M-估计,用回切方法给出了函数的M-估计.证明了该估计的渐近正态性,并通过模拟验证了所提出方法的优良性.Partial linear models have been discussed by many people and applied widely in many fields.Many approaches are developed to estimate the unknown parameters and the unknown functions,but these approaches are lack of robustness.The robust M-estimation on partial linear models was studied.The estimator of parametric component was developed by using local M-estimation method and average method,the estimator of nonparametric component was given by back fitting method.Asymptotic normality of these estimators was investigated.One simulation shows the effectiveness of the proposed procedure.

关 键 词：部分线性模型 M-估计 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]