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{1176347745,
author = {McKeague, Ian W. and Utikal, Klaus J.},
title = {Inference for a Nonlinear Counting Process Regression Model},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 1172-1187},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347745}
}
McKeague, Ian W.; Utikal, Klaus J. Inference for a Nonlinear Counting Process Regression Model. Ann. Statist., Tome 18 (1990) no. 1, pp. 1172-1187. http://gdmltest.u-ga.fr/item/1176347745/