删失数据的光滑乘积限估计的渐近性质  

Asymptotic Behavior of the Smooth Product-limit Estimator under Random Censorship

作　　者：周勇[1] 

机构地区：[1]北京大学概率统计系,中国科学院应用数学研究所青年概率统计实验室

出　　处：《数学学报（中文版）》1996年第2期238-246,共9页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：在删失数据的模型下，对于光滑未知的分布函数Ｆ０，文中提出了光滑化的方法去估计Ｆ０，得到了光滑ＰＬ估计Ｆｎ，并建立了Ｆｎ在Ｄ（－∞，Ｔ），Ｔ＜ＴＦ上的弱收敛和强相合的结果．同时也获得了光滑ＰＬ过程的强逼近和重对数律．Weak convergence and strong consistency are established for a smooth version of the classical product-limit estimator of a distribution function when the data are subject to random censorship. The weak convergences oil D(I) = D(-∞,T] for T < TF=inf{x: F(x)=1} are shown to hold for the entire interval I under basically the same assumptions that have been used in the literature to establish the weak convergence of normalized estimator in D(I). Moreover,strong approximations and the laws of the iterated logarithm are proved.

关 键 词：重对数律 光滑PL过程 乘积限估计 渐近性 

分 类 号：O212.1[理学—概率论与数理统计]