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Asymptotics for posterior hazards

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  • Pierpaolo De Blasi
  • Giovanni Peccati
  • Igor Prünster
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    Abstract

    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.

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    File URL: http://www.carloalberto.org/assets/working-papers/no.122.pdf
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    Bibliographic Info

    Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 122.

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    Length: 40 pages
    Date of creation: 2009
    Date of revision:
    Handle: RePEc:cca:wpaper:122

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    Related research

    Keywords: Bayesian Consistency; Bayesian Nonparametrics; Central limit theorem; Completely random measure; Path-variance; Random hazard rate; Survival analysis;

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    Cited by:
    1. Stefano Favaro & Antonio Lijoi & Igor Prunster, 2011. "Asymptotics for a Bayesian nonparametric estimator of species richness," Quaderni di Dipartimento 144, University of Pavia, Department of Economics and Quantitative Methods.
    2. Antonio Lijoi & Bernardo Nipoti, 2013. "A class of hazard rate mixtures for combining survival data from different experiments," DEM Working Papers Series 059, University of Pavia, Department of Economics and Management.
    3. Ilenia Epifani & Antonio Lijoi, 2009. "Nonparametric Priors for Vectors of Survival Functions," Quaderni di Dipartimento 098, University of Pavia, Department of Economics and Quantitative Methods.

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