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Linear and Quadratic Functionals of RandomHazard rates: an Asymptotic Analysis

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  • Giovanni Peccati
  • Igor Prünster

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.

Suggested Citation

  • Giovanni Peccati & Igor Prünster, 2006. "Linear and Quadratic Functionals of RandomHazard rates: an Asymptotic Analysis," ICER Working Papers - Applied Mathematics Series 33-2006, ICER - International Centre for Economic Research.
    • Handle: RePEc:icr:wpmath:33-2006
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    File URL: http://www.bemservizi.unito.it/repec/icr/wp2006/ICERwp33-06.pdf
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    References listed on IDEAS

    as
    1. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
    2. Ishwaran, Hemant & James, Lancelot F., 2004. "Computational Methods for Multiplicative Intensity Models Using Weighted Gamma Processes: Proportional Hazards, Marked Point Processes, and Panel Count Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 175-190, January.
    3. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
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