Right censoring and martingale methods for failure time data. (English) Zbl 0688.62047

Jacobsen, Martin

Ann. Stat. 17, No. 3, 1133-1156 (1989).

Summary: Statistical models are considered for (partial) observation of independent, identically distributed failure times, subjected to censoring from the right. A minimal class of censoring patterns is determined under the assumption that the failure intensities are as they would have been without censoring. This class is then used to discuss the statistical models for right censored survival data, where, e.g., the Kaplan-Meier estimator exploits all available information about the failure time distribution. The counting process description of survival data is used throughout.

MSC:

62M09	Non-Markovian processes: estimation
62G05	Nonparametric estimation
62N05	Reliability and life testing
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

intensity process; multiplicative intensity model; martingale estimator; independent, identically distributed failure times; minimal class of censoring patterns; right censored survival data; Kaplan-Meier estimator; failure time distribution; counting process description of survival data