随机加权法和稳健性  

The Random Weighting Method and Robustness

作　　者：朱燕堂[1] 戎海武[1] 

机构地区：[1]西北工业大学

出　　处：《工程数学学报》1991年第1期85-93,共9页Chinese Journal of Engineering Mathematics

摘　　要：设X_1,X_2,……是一个i.i.d.随机变量序列,其公共分布为F,F_n为其对应的经验公布函数,H_a是F_n的随机加权估计,又设T(F)是一个泛函,其对应的估计量是T(F_n),随机加权估计量为T(H_n).按照[4],[7]关于定性稳健性和稳健正态性的定义,本文指出了T(H_n)的定性稳健性的充要条件和弱收敛速度,作为特例,本文还讨论了L统计量的随机加权估计序列的定性稳健性和稳健正态性。Let X1,X2…,be a sequence of i.i.d.random variables, the common distribution function of Xi is F0. Let Fn be the empirical distribution and Hn be the random weighting estimate of Fm. Let T be a functional, according to the definitions of qualitative robustness and robust normality in reference [4] [7], this paper gives the necessary and sufficient condition of the qualitative robustness of T(Hn)and the weak convcrgancc speed of T(Hn). Taking for an example, this paper proves the qualitative robustness and robust normality of the random weighting estimate sequence of L-statistic.

关 键 词：随机加权法 稳健性 L统计量 

分 类 号：O212[理学—概率论与数理统计]