The Annals of Statistics

Cox's Periodic Regression Model

O. Pons and E. de Turckheim

Full-text: Open access

Abstract

Cox's regression model has been successfully used for censored survival data. It can be adapted to model a counting process having a periodic underlying intensity. In survival analysis, the asymptotic properties, as studied by Andersen and Gill, correspond to a large number of processes running parallel over the same time interval. Here a single point process is observed over a large number of successive periods. Cox's model can easily be adapted to this situation and conditions are given which ensure the estimators have the classical large sample properties. Proofs use both martingale techniques and theorems for convergence of empirical probability measures. Finally, an example concerning the feeding pattern of domestic rabbits is included.

Article information

Source
Ann. Statist., Volume 16, Number 2 (1988), 678-693.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350828

Digital Object Identifier
doi:10.1214/aos/1176350828

Mathematical Reviews number (MathSciNet)
MR947570

Zentralblatt MATH identifier
0664.62099

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62G05: Estimation 62M99: None of the above, but in this section 62P10: Applications to biology and medical sciences

Keywords
Intensity martingale weak convergence of stochastic processes ergodicity mixing processes periodic feeding pattern

Citation

Pons, O.; de Turckheim, E. Cox's Periodic Regression Model. Ann. Statist. 16 (1988), no. 2, 678--693. doi:10.1214/aos/1176350828. https://projecteuclid.org/euclid.aos/1176350828


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