线性模型中M估计分布的随机加权方法逼近  

APPROXIMATING THE DISTRIBUTION OF M-ESTIMATORS IN LINEAR MODELS BY RANDOMLY WEIGHTED BOOTSTRAP

作　　者：吴小燕[1] 赵林城[1] 杨亚宁[1] 

机构地区：[1]中国科学技术大学统计与金融系,合肥230026

出　　处：《系统科学与数学》2008年第9期1092-1100,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10471136)资助课题.

摘　　要：在线性模型中,M估计的渐近分布通常都涉及到不易估计的未知误差分布的某些量,如果要估计渐近方差,就需对这些冗余参数进行估计.利用随机加权方法可以避免先对误差分布中的冗余参数进行估计.给出了当自变量是随机变量时,M估计分布的随机加权逼近,证明了M估计分布的随机加权逼近是一致相合的.当取不同的凸函数,样本大小和随机权时,进一步利用蒙特卡洛方法研究估计分布.研究表明随机权取泊松权时,不仅达到同样的效果而且可以减小计算量.The asymptotic distribution of the M-estimators are generally related to quantities of the error distribution that can not be conveniently estimated. The randomly weighted bootstrap method provides a way of assessing the distribution of the M-estimators without estimating the nuisance quantities of the error distributions. In this paper, the distribution of M-estimators is approximated by the randomly weighted bootstrap method in linear models when the covariates are random. It is shown that the randomly weighted bootstrapping estimation of the distribution of the M-estimator is uniformly consistent. Also, the variance estimates is investigated by Monte Carlo simulations for different choices of the convex function, sample size and random weights. Poisson weighting is recommended for reducing the computational burden in the randomly weighted bootstrapping M-estimators.

关 键 词：线性模型 M估计 随机加权 

分 类 号：O212.1[理学—概率论与数理统计] O211.5[理学—数学]