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Nonparametric Estimation under Censoring and Passive Registration

机译:删失与被动配准下的非参数估计

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The classical random censorship model assumes that we follow an individual continuously up to the time of failure or censoring, so observing this time as well as the indicator of its type. Under passive registration we only get information on the state of the individual at random observation or registration times. In this paper we assume that these registration times are the times of events in an independent Poisson process, stopped at failure or censoring; the time of failure is also observed if not censored. This problem turns up in historical demography, where the survival time of interest is the life-length, censoring is by emigration, and the observation times are times of births of children, and other life-events. (Church registers contain dates of births, marriages, deaths, but not emigrations.) The model is shown to be related to the problem of estimating a density known to be monotone. This leads to an explicit description of the non-parametric maximum likelihood estimator of the survival function (based on i.i.d. observations from this model) and to an analysis of its large sample properties.
机译:经典的随机检查模型假设我们一直跟踪某个人,直到失败或检查为止,因此要观察该时间及其类型的指示器。在被动注册下,我们仅在随机观察或注册时间获得有关个人状态的信息。在本文中,我们假设这些注册时间是在独立的Poisson流程中发生的事件的时间,在失败或检查时停止。如果没有审查,也会观察到故障时间。这个问题在历史人口学中出现,其中感兴趣的生存时间是一生的寿命,审查是通过移民进行的,观察时间是孩子的出生时间以及其他生活事件。 (教堂登记册上载有出生,结婚,死亡的日期,但不包括移民的日期。)该模型与估计单调密度的问题有关。这导致了对生存函数的非参数最大似然估计器的明确描述(基于该模型的i.i.d观察),并对其大型样本属性进行了分析。

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