The Annals of Statistics

Inference for a Nonlinear Counting Process Regression Model

Ian W. McKeague and Klaus J. Utikal

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Martingale and counting process techniques are applied to the problem of inference for general conditional hazard functions. This problem was first studied by Beran, who introduced a class of estimators for the conditional cumulative hazard and survival functions in the special case of time-independent covariates. Here the covariate can be time dependent; the classical i.i.d. assumptions are relaxed by replacing them with certain asymptotic stability assumptions, and models involving recurrent failures are included. This is done within the framework of a general nonparametric counting process regression model. Important examples of the model include right-censored survival data, semi-Markov processes, an illness-death process with duration dependence, and age-dependent birth and death processes.

Article information

Ann. Statist., Volume 18, Number 3 (1990), 1172-1187.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62J02: General nonlinear regression 62G05: Estimation

Conditional hazard function censored survival data counting processes semi-Markov processes martingale central limit theorem


McKeague, Ian W.; Utikal, Klaus J. Inference for a Nonlinear Counting Process Regression Model. Ann. Statist. 18 (1990), no. 3, 1172--1187. doi:10.1214/aos/1176347745.

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