Open Access
Translator Disclaimer
October 2008 Linear and quadratic functionals of random hazard rates: An asymptotic analysis
Giovanni Peccati, Igor Prünster
Ann. Appl. Probab. 18(5): 1910-1943 (October 2008). DOI: 10.1214/07-AAP509


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.


Download Citation

Giovanni Peccati. Igor Prünster. "Linear and quadratic functionals of random hazard rates: An asymptotic analysis." Ann. Appl. Probab. 18 (5) 1910 - 1943, October 2008.


Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1153.60028
MathSciNet: MR2462554
Digital Object Identifier: 10.1214/07-AAP509

Primary: 60G57 , 62G20

Keywords: asymptotics , Bayesian nonparametrics , central limit theorem , completely random measure , multiple Wiener–Itô integral , path-variance , random hazard rate , Survival analysis

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.18 • No. 5 • October 2008
Back to Top