Asymptotics for Posterior Hazards
An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive a...
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| Veröffentlicht in: | The Annals of statistics 2009-08, Vol.37 (4), p.1906-1945 |
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| container_end_page | 1945 |
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| container_issue | 4 |
| container_start_page | 1906 |
| container_title | The Annals of statistics |
| container_volume | 37 |
| creator | De Blasi, Pierpaolo Peccati, Giovanni Prünster, Igor |
| description | An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals. |
| doi_str_mv | 10.1214/08-AOS631 |
| format | Article |
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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | 60G57 62G20 Asymptotic methods Asymptotics Bayesian analysis Bayesian consistency Bayesian nonparametrics Censorship Central limit theorem completely random measure Determinism Distribution theory Exact sciences and technology General topics Hazards Mathematical functions Mathematics Nonparametric inference Nonparametric models path-variance Probability and statistics Probability theory and stochastic processes random hazard rate Random variables Sample size Sciences and techniques of general use Statistical variance Statistics Stochastic processes Studies Sufficient conditions Survival analysis |
| title | Asymptotics for Posterior Hazards |
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