We study nonparametric estimation with two types of data structures. In the first data structure n i.i.d. copies of (C, N(C)) are observed, where N is a finite state counting process jumping at time-variables of interest and C a random monitoring time. In the second data structure n i.i.d. copies of (C ∧ T, I (T ≤ C), N(C ∧ T)) are observed, where N is a counting process with a final jump at time T (e.g., death). This data structure includes observing right-censored data on T and a marker variable at the censoring time.In these data structures, easy to compute estimators, namely (weighted)-pool-adjacent-violator estimators for the marginal distributions of the unobservable time variables, and the Kaplan–Meier estimator for the time T till the final observable event, are available. These estimators ignore seemingly important information in the data. In this paper we prove that, at many continuous data generating distributions the ad hoc estimators yield asymptotically efficient estimators of -estimable parameters.
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机译:我们研究两种类型的数据结构的非参数估计。在第一数据结构中,观察到(C,N(C))的副本,其中N是在感兴趣的时间变量处跳跃的有限状态计数过程,C是随机监视时间。在第二数据结构中,观察到(C∧T,I(T≤C),N(C∧T))的副本,其中N是一个计数过程,最终在时间T处跳跃(例如死亡)。该数据结构包括在审查时观察T上的右删失数据和标记变量。在这些数据结构中,易于计算的估计量,即(可加权的)池-相邻-违反者估计量,用于不可观察的时间变量的边际分布,以及直到最后可观测事件的时间 T em>的Kaplan–Meier估计器。这些估算器忽略了数据中看似重要的信息。在本文中,我们证明,在许多连续的数据生成分布中,临时估计量产生了展开▼