随机加权法的强逼近及其应用  

STRONG APPROXIMATION OF RANDOM WEIGHTING METHODS AND ITS APPLICATION

作　　者：周勇[1] 邹植民[1] 

机构地区：[1]湘潭师范学院,湖南411100

出　　处：《应用概率统计》1993年第2期130-137,共8页Chinese Journal of Applied Probability and Statistics

基　　金：湖南省教委第1490201资金资助

摘　　要：本文研究了由随机加权法产生的经验过程及分位点过程的强逼近。In this paper, we get the rate of strong approximation of Random Weighting Methods on the empirical process and the quantile process, i.e. under some conditions, we have, |α_n(x)-B_n(F(x))|=O(ι(n)) a.s.P~* |α_n(x)-n^(-1/2)K(F(x), n)|=O(ι(n)) a.s.P~* |f(F^(-1)(t))Q_n~*(t)-B_n(t)|=O(ι(n)) a.s.P~* |f(F^(-1)(t))Q_n~*(t)-n^(-1/2)K(t, n)|=O(ι(n)) a.s P~* where α_n(x), Q_n~*(t), B_n(x)and n^(-1/2)K(t, n) are the empirical process, the quantile process, Brownian bridge and Kiefer process respectively.

关 键 词：随机加权法 强逼近 经验过程 

分 类 号：O211.6[理学—概率论与数理统计]