The Annals of Statistics

Inference for a Nonlinear Counting Process Regression Model

Ian W. McKeague and Klaus J. Utikal

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347745

Digital Object Identifier
doi:10.1214/aos/1176347745

Mathematical Reviews number (MathSciNet)
MR1062704

Zentralblatt MATH identifier
0721.62087

JSTOR
links.jstor.org

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176347745


Export citation