Book ChapterDOI
Weak Convergence of the Aalen Estimator for a Censored Renewal Process
Thomas Sellke
- pp 183-194
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The article was published on 1988-01-01. It has received 31 citations till now. The article focuses on the topics: Weak convergence & Renewal theory.read more
Citations
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Journal ArticleDOI
Nonparametric Estimation With Recurrent Event Data
TL;DR: In this article, the problem of nonparametric estimation for the distribution function governing the time to occurrence of a recurrent event in the presence of censoring is considered, and the authors derive Nelson-Aalen and Kaplan-Meier-type estimators and establish their respective finite-sample and asymptotic properties.
Journal ArticleDOI
Semiparametric Inference for a General Class of Models for Recurrent Events.
TL;DR: The results indicate that the flexibility of this general class of models provides a safeguard for analyzing recurrent event data, even data possibly arising from a frailtyless mechanism.
Journal ArticleDOI
Dynamic Modeling and Statistical Analysis of Event Times
TL;DR: This review article provides an overview of recent work in the modelling and analysis of recurrent events arising in engineering, reliability, public health, biomedical, and other areas and describes a recent general class of models for recurrent events which simultaneously accommodates these aspects.
Journal ArticleDOI
A General Class of Parametric Models for Recurrent Event Data
Russell S. Stocker,Edsel A. Peña +1 more
TL;DR: The general class of models proposed by Peña and Hollander for recurrent event data is considered under a fully parametric specification of the baseline hazard rate function and under the two cases where the model does and does not incorporate frailty components.
Book ChapterDOI
A Weak Convergence Result Relevant in Recurrent and Renewal Models
TL;DR: In this paper, the authors prove a general weak convergence result useful for establishing the distributional properties of processes, estimators, or test statistics arising in recurrent event and renewal process models.
References
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Journal ArticleDOI
On Tail Probabilities for Martingales
TL;DR: In this paper, the Laplace transform of the crossing time of a martingale with uniformly bounded increments is shown to have the same distribution as the distribution of crossing times of Brownian motion, even in the tail.
Book
Censoring and stochastic integrals
TL;DR: The second edition of the book as mentioned in this paper is 76 pages longer than the first and has a 50-page appendix entitled, "A Review of Fundamental Concepts" which contains examples and problems from the fields of biology and medicine and unless one is fairly familiar with these subject areas, the example and problems will not be very meaningful.
Journal ArticleDOI
A proof of optimality for age replacement policies
TL;DR: In this article, the authors proved that the age replacement policy (ARP) is the optimal decision rule among all reasonable policies for stochastically failing units, and that the ARP is the best policy to minimize the objective function under discussion.