样本均值随机加权估计的渐近性质  

ASYMPTOTIC PROPERTIES OF THE RANDOM WEIGHTING ESTIMATE OF THE SAMPLING MEAN

作　　者：温显斌[1] 石坚[2] 朱燕堂[3] 

机构地区：[1]山东工程学院基础部,淄博255012 [2]中国科学院系统科学研究所,北京100080 [3]西北工业大学应用数学系,西安710072

出　　处：《系统科学与数学》1998年第3期347-352,共6页Journal of Systems Science and Mathematical Sciences

摘　　要：本文给出了样本均值随机加权估计的条件分布以概率（几乎处处）收敛到正态分布的充要条件为X1属于正态吸收域D（2）（E（X^2_1）＜∞）；并且进一步证明了当样本具有缓慢变化的尾时，样本均值随机加权估计之条件分布以概率收敛到非退化分布．In this paper, we show the necessary and sufficient condition for convergence in probability (a.s.) of the distribution function of a random weighting mean is that the sampling comes from the domain of attraction of normal distribution (EX^2_1 < ∞). Further, we show that when X1 is slowly varying, the distribution of random weighting estimate of the mean converges in probability to nondegenerate distribution.

关 键 词：随机加权法 吸收域 样本均值 渐近性质 估计 

分 类 号：O211.67[理学—概率论与数理统计]