Estimating the expected total number of events in a process

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	Estimating the expected total number of events in a process
	Maller, RA ; Sun, LQ; Zhou, X
	2002-06-01
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	97 期号:458 页码:577-589
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 the age 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.
关键词	age profile censored observations cumulative mean function Kaplan-Meier estimator Nelson-Aalen estimator recurrent process
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000176078300024
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/17550
专题	应用数学研究所
通讯作者	Maller, RA
作者单位	1.Univ Western Australia, Dept Accounting & Finance, Nedlands, WA 6907, Australia 2.Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Peoples R China
推荐引用方式 GB/T 7714	Maller, RA,Sun, LQ,Zhou, X. Estimating the expected total number of events in a process[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2002,97(458):577-589.
APA	Maller, RA,Sun, LQ,&Zhou, X.(2002).Estimating the expected total number of events in a process.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,97(458),577-589.
MLA	Maller, RA,et al."Estimating the expected total number of events in a process".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 97.458(2002):577-589.