On Some Questions Of Interval-cersored Data

In reliability and survival analysis, the data obtained in modeling failure time is often interval censored. They are namely as interval-censored dataA. The exact occurrence time of an event is not observed, but what is known is the interval in which the event took place. In a research, before the left vertex, we can observe exact occurrenc e time After the left vertex, we know exact occurrence time is in the interval or bigger than the right vertex. They are namely as interval-censored dataB.Recently there is an enormous amount of literature on interval-censored dataA. In these studies, nonparametric likelihood estimation are widely used in estimating distribution function or regression parameters. These estimators all have the likelihood function and in most situations we can only use iterative operations to get an approximate solution. According to the unbiased transformation method, we study interval-censored dataB by the same method.As to the characteristic of interval-censored, studying the survival analysis written by Zheng Zukuang, suggested by the idea of ClassK method, have mainly done three tasks:First,deal with the exactitude observed data and interval-censored,letY^(r)=Φ₁(Y)δ₁+δ₂(U,V)Φ₂+δ₃(V)(1-δ₁-δ₂),where (u,v) is the random interval-censored variable of y,δ₁=I_(Y≤U),δ₂=I_{(U.According the rule of EY^(r)=EY^r,find the condition whichΦ1(·),Φ2(·,·),Φ3(·) need satisfy, put those satisfied in one species, that is ClassX method, and the estimators have strong consistent and asymptotic normality. Second,ClassX was proved not empty and meaningful.According to the condition of limited variance of the estimators the rth original mement of interval-censored dataA, we get the condition of limited variance of the estimators the rth original mement of interval-censoredB data and right-censored data. And get variance of the interval-censored variable. Third, when the failure time is interval -censored dataAand censored dataB, we estimate EY^r when the interval -censored variable (u,v) is same. The information of interval-censored dataB more than interval-censored dataA, so we compare the variance of the estimators the rth original mement of the interval-censored dataB with interval-censored dataA. And we get the condition which the variance of the rth original mement of interval-censoredB is smaller, so we can observe the failure time by choicing better method.}