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Asymptotics for posterior hazards. (English) Zbl 1168.62042

Summary: 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. We provide a comprehensive analysis of the asymptotic behavior of such models. We investigate the 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.

MSC:

62G20 Asymptotic properties of nonparametric inference
62F15 Bayesian inference
60F05 Central limit and other weak theorems
60G57 Random measures
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