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February 1998 Asymptotic theory for the correlated gamma-frailty model
Erik Parner
Ann. Statist. 26(1): 183-214 (February 1998). DOI: 10.1214/aos/1030563982

Abstract

The frailty model is a generalization of Cox's proportional hazard model, where a shared unobserved quantity in the intensity induces a positive correlation among the survival times. Murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator (NPMLE) for the shared gamma-frailty model without covariates. In this paper we extend this result to the correlated gamma-frailty model, and we allow for covariates. We discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator, which goes back to Wald. Our proof of the consistency for the NPMLE is essentially the same as the classical proof for the maximum likelihood estimator. A new central limit theorem for processes of bounded variation is given. Furthermore, we prove that a consistent estimator for the asymptotic variance of the NPMLE is given by the inverse of a discrete observed information matrix.

Citation

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Erik Parner. "Asymptotic theory for the correlated gamma-frailty model." Ann. Statist. 26 (1) 183 - 214, February 1998. https://doi.org/10.1214/aos/1030563982

Information

Published: February 1998
First available in Project Euclid: 28 August 2002

zbMATH: 0934.62101
MathSciNet: MR1611788
Digital Object Identifier: 10.1214/aos/1030563982

Subjects:
Primary: 62M09
Secondary: 62G05

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 1 • February 1998
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