The Annals of Statistics

Cox's Periodic Regression Model

O. Pons and E. de Turckheim

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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

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

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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

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


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

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