Inference for a Nonlinear Counting Process Regression Model
Ian W. McKeague, Klaus J. Utikal
The Annals of Statistics · 1990 · Volume 18 · Issue 3
Abstract
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.
Keywords
62G05, 62J02, 62M09, Censored survival data, Conditional Hazard function, counting processes, martingale central limit theorem, Semi-Markov processes
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