The Annals of Statistics

Asymptotics for posterior hazards

Pierpaolo De Blasi, Giovanni Peccati, and Igor Prünster

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Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 4 (2009), 1906-1945.

Dates
First available in Project Euclid: 18 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1245332836

Digital Object Identifier
doi:10.1214/08-AOS631

Mathematical Reviews number (MathSciNet)
MR2533475

Zentralblatt MATH identifier
1168.62042

Subjects
Primary: 62G20: Asymptotic properties 60G57: Random measures

Keywords
Asymptotics Bayesian consistency Bayesian nonparametrics central limit theorem completely random measure path-variance random hazard rate survival analysis

Citation

De Blasi, Pierpaolo; Peccati, Giovanni; Prünster, Igor. Asymptotics for posterior hazards. Ann. Statist. 37 (2009), no. 4, 1906--1945. doi:10.1214/08-AOS631. https://projecteuclid.org/euclid.aos/1245332836


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