The Annals of Applied Probability

Linear and quadratic functionals of random hazard rates: An asymptotic analysis

Giovanni Peccati and Igor Prünster

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Abstract

A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results for linear and quadratic functionals of such random hazard rates. In particular, we prove central limit theorems for the cumulative hazard function and for the path-second moment and path-variance of the hazard rate. Our techniques are based on recently established criteria for the weak convergence of single and double stochastic integrals with respect to Poisson random measures. The findings are illustrated by considering specific models involving kernels and random measures commonly exploited in practice. Our abstract results are of independent theoretical interest and can be applied to other areas dealing with Lévy moving average processes. The strictly Bayesian analysis is further explored in a companion paper, where our results are extended to accommodate posterior analysis.

Article information

Source
Ann. Appl. Probab., Volume 18, Number 5 (2008), 1910-1943.

Dates
First available in Project Euclid: 30 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1225372956

Digital Object Identifier
doi:10.1214/07-AAP509

Mathematical Reviews number (MathSciNet)
MR2462554

Zentralblatt MATH identifier
1153.60028

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

Keywords
Asymptotics Bayesian nonparametrics central limit theorem completely random measure multiple Wiener–Itô integral path-variance random hazard rate survival analysis

Citation

Peccati, Giovanni; Prünster, Igor. Linear and quadratic functionals of random hazard rates: An asymptotic analysis. Ann. Appl. Probab. 18 (2008), no. 5, 1910--1943. doi:10.1214/07-AAP509. https://projecteuclid.org/euclid.aoap/1225372956


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