Linear and Quadratic Functionals of RandomHazard rates: an Asymptotic Analysis

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. We illustrate our results by considering specific models involving kernels and random measures commonly exploited in practice.Asymptotics; Bayesian Nonparametrics; Central limit theorem; Path–variance; Random hazard rate; Survival analysis; Completely random measure; Multiple Wiener-Ito integral.