ESTIMATING A DISTRIBUTION FUNCTION WITH TRUNCATED AND CENSORED-DATA
ESTIMATING A DISTRIBUTION FUNCTION WITH TRUNCATED AND CENSORED-DATA
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DOI：
10.1214/aos/1176347991
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发表时间：
1991-03-01
影响因子：
4.5
通讯作者：
YING, ZL
中科院分区：
文献类型：
--
作者：
LAI, TL;YING, ZL
对乘积极限估计器提出了一个小的修改，用于估计一个分布函数(不一定是连续的)，当数据通过独立但不一定同分布的截尾-截尾变量被截断或截尾或两者同时被截断或截尾时。利用鞅积分表示和经验过程理论，建立了估计量的一致强相合性，并证明了函数在整个可观测范围内的弱收敛结果。数值结果也说明了这种修正的有效性，特别是在截断数据的情况下。
A minor modification of the product-limit estimator is proposed for estimating a distribution function (not necessarily continuous) when the data are subject to either truncation or censoring, or to both, by independent but not necessarily identically distributed truncation-censoring variables. Making use of martingale integral representations and empirical process theory, uniform strong consistency of the estimator is established and weak convergence results are proved for the entire observable range of the function. Numerical results are also given to illustrate the usefulness of the modification, particularly in the context of truncated data.