缺失数据下局部M-估计的相合性和渐近正态性  

Consistency and asymptotic normality of local M-estimator in case of response data missing

作　　者：罗双华[1] 庞淑侠[2] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050 [2]兰州理工大学计算机与通信学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2006年第4期145-148,共4页Journal of Lanzhou University of Technology

摘　　要：在缺失响应变量的不完全数据下,对非参数回归模型进行研究,利用稳健的变窗宽局部线性回归的方法,给出了回归函数m(x)的估计,并证明了局部M-估计具有相合性和渐近正态性.所提出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.并且使用变窗宽提高了所得M-估计的可塑性,使之能成功地处理空间非齐次曲线、异方差性及非均匀设计密度.所得估计的渐近结果为求渐近最优方案以及直接从数据估计最优变窗宽提供了理论基础.The nonparametric regressive model was investigated in the case of response data missing. A estimation of m（x） was given by using a robust local linear regression smoother with variable bandwidth. It was also verified that the proposed M-estimator possessed asymptotical normality and consistency. The proposed method inherited the merits of local polynomial regression and overcame the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhanced the flexibility of the local M-estimators obtained and made them possible to cope well with spatially inhomogeneous curves, heteroscedustic errors,and non-uniform design densities. The asymptotic results of the estimation provided a theoretical basis for finding the asymptotic optimal scheme as well as estimating the optimal variable band- width directly from the data.

关 键 词：局部线性回归 M-估计 缺失数据 变窗宽 渐近正态性 相合性 

分 类 号：O211.4[理学—概率论与数理统计]