ASYMPTOTICS FOR POSTERIOR HAZARDS

• 成果类型: Article
• 署名作者: De Blasi, Pierpaolo; Peccati, Giovanni; Prunster, Igor
• 署名单位: University of Turin; Universite Paris Nanterre; Universite Paris Saclay
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS631
• 发表日期: 2009
• 页码: 1906-1945
• 关键词: bayesian consistency; STOCHASTIC INTEGRALS; survival analysis; models; distributions; estimators; mixtures

摘要

An important issue in survival analysis is the investigation and the modeling of hazard rates. Within a Bayesian nonparametric framework, a natural and popular approach is to model hazard rates as kernel mixtures with respect to a completely random measure. In this paper we provide a comprehensive analysis of the asymptotic behavior of such models. We investigate consistency of the posterior distribution and derive fixed sample size central limit theorems for both linear and quadratic functionals of the posterior hazard rate. The general results are then specialized to various specific kernels and mixing measures yielding consistency under minimal conditions and neat central limit theorems for the distribution of functionals.