Estimating the Expected Total Number of Events in a Process
估计重复事件过程的期望总事件数AI 解读 ↓
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估计重复事件过程的期望总事件数
- 研究问题
- 当个体重复事件过程可能在有限时间后停止时，如何估计随年龄累积的平均事件数，并从有限随访中估计期望总事件数？
- 方法与思路
- 作者利用事件间隔分布的 Kaplan–Meier 估计构造年龄轨迹估计量，分析其渐近性质，并与 Nelson–Aalen 累积均值估计比较。
- 材料陈述的贡献
- 摘要称，充分随访与该估计量的一致性存在充要关系，另有条件性渐近正态结果；模拟和实例提示其总事件数估计更稳定。
- 阅读关注点
- 应核对充分随访的严格定义、间隔分布与删失条件，以及轨迹末端趋平的实践表现如何区别于一致性的正式条件。
- 阅读边界
- 仅依据稿件版本未注明的 OpenAlex 索引摘要；具体条件和比较数值未说明，模拟优势不能推广为普遍优越，轨迹趋平也不能单独证明随访充分。
原文摘要
We consider estimation of the cumulative mean function of a process recurring in time, such as the numbers of arrests or migrations accrued by an individual, as a function of their age. We call this theage profile of a series of events. In some situations we can expect a finite value for the total number of events experienced by an individual, for example, when the distribution of the interevent times is improper, so that the process may cease at a finite time with positive probability. We propose and analyze a new estimator, constructed from Kaplan–Meier (KM) estimators of the interevent time distributions, for such an age profile, and compare it with the Nelson–Aalen (NA) estimator of the cumulative mean function of a process. The KM estimator is proved to be uniformly consistent for the age profile if and only if follow-up in the sample is sufficient in a sense that is manifested in practice by the leveling off of the profiles at their right-side ends, and is asymptotically normally distributed around its true value under mild conditions. Simulation results suggest that it is generally a better estimator than the NA estimator for the total number of events. It also appears to be more stable when applied to real data examples. For accurate estimation, it seems to be important to select a cohort of individuals whose ages at the first event are as similar as possible. The estimators are illustrated on some time-to-arrest data.