The Annals of Statistics
- Ann. Statist.
- Volume 26, Number 1 (1998), 183-214.
Asymptotic theory for the correlated gamma-frailty model
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.
Ann. Statist., Volume 26, Number 1 (1998), 183-214.
First available in Project Euclid: 28 August 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Parner, Erik. Asymptotic theory for the correlated gamma-frailty model. Ann. Statist. 26 (1998), no. 1, 183--214. doi:10.1214/aos/1030563982. https://projecteuclid.org/euclid.aos/1030563982