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

Citation
Peccati, Giovanni et Prünster, Igor, Linear and quadratic functionals of random hazard rates: An asymptotic analysis, Annals of applied probability , 18(5), 2008, pp. 1910-1943
ISSN journal
10505164
Volume
18
Issue
5
Year of publication
2008
Pages
1910 - 1943
Database
ACNP
SICI code
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.