LINEAR AND QUADRATIC FUNCTIONALS OF RANDOM HAZARD RATES: AN ASYMPTOTIC ANALYSIS

• 成果类型: Article
• 署名作者: Peccati, Giovanni; Prunster, Igor
• 署名单位: Sorbonne Universite; University of Turin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP509
• 发表日期: 2008
• 页码: 1910-1943
• 关键词: bayesian-analysis; STOCHASTIC INTEGRALS; survival analysis; models; distributions; CONVERGENCE; estimators; inference; calculus

摘要

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 Levy moving average processes. The strictly Bayesian analysis is further explored in a companion paper, where our results are extended to accommodate posterior analysis.