The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Asymptotic theory for the correlated gamma-frailty model
Open accessAbstract
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.
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Cites
Rudin, W. (1973) · Cited by 13,740
Weak Convergence and Empirical Processes
van der Vaart, A. W., & Wellner, J. A. (1996) · Springer Series in Statistics · doi:10.1007/978-1-4757-2545-2 · Cited by 5,014
Cox’s regression model for counting processes: A large sample study
Andersen, P. K., & Gill, R. D. (1982) · The Annals of Statistics · doi:10.1214/aos/1176345976 · Cited by 4,419
Statistical Models Based on Counting Processes
Bry, X., Andersen, P. K., Borgan, Ø., Gill, R. D., Keiding, N., & Borgan, O. (1997) · Population (French Edition) · doi:10.2307/1534625 · Cited by 2,884
Statistical Models Based on Counting Processes
Andersen, P. K., Borgan, Ø., Gill, R. D., & Keiding, N. (1993) · Springer Series in Statistics · doi:10.1007/978-1-4612-4348-9 · Cited by 2,855
The impact of heterogeneity in individual frailty on the dynamics of mortality
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Note on the Consistency of the Maximum Likelihood Estimate
Wald, A. (1949) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729952 · Cited by 1,100
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Cited by
Murphy, S. A., & Van Der Vaart, A. W. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10474219 · Cited by 712
Frailty Models in Survival Analysis
Wienke, A. (2010) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420073911 · Cited by 454
Shared Frailty Models for Recurrent Events and a Terminal Event
Liu, L., Wolfe, R. A., & Huang, X. (2004) · Biometrics · doi:10.1111/j.0006-341x.2004.00225.x · Cited by 342
Metadata
- Authors
- Parner, E.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1998-02-01
- Volume
- 26
- Issue
- 1
- Pages
- 183-214
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2008704042
- Cited by
- 269
- References
- 19
- FWCI
- 8.32
- Type
- journal article
- Language
- en
- Open access
- bronze
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