Skip to main content
Log in

Bootstrapping a Bayes estimator of a survival function with censored data

  • Bayesian Procedure
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

The large-sample frequentist property of a frequentist bootstrap for a posterior mean with respect to a Dirichlet prior of the survival function for a randomly censored data is given. The weak convergence of a bootstrap version of the Susarla-Van Ryzin estimator is established on the whole real line. An illustration of the technique and some Monte Carlo studies are also given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Akritas, M. G. (1986). Bootstrapping the Kaplan-Meier estimator,J. Amer. Statist. Assoc.,81, 1032–1038.

    Google Scholar 

  • Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.

    Google Scholar 

  • Breslow, N. and Crowley, J. (1974). A large sample study of the life table and product-limit estimates under random censorship,Ann. Statist.,2, 437–453.

    Google Scholar 

  • Efron, B. (1981). Censored data and the bootstrap,J. Amer. Statist. Assoc.,76, 312–319.

    Google Scholar 

  • Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems,Ann. Statist.,1, 209–230.

    Google Scholar 

  • Ferguson, T. S., Phadia, E. G. and Tiwari, R. C. (1992). Bayesian nonparametric inference,Current Issues in Statistical Inference: Essays in Honor of D. Basu (eds. M. Ghosh and P. K. Pathak), IMS Lecture Note & Monograph Series, Vol. 17, 127–150.

  • Gill, R. D. (1980). Censoring and Stochastic Integrals, Mathematical Centre Tract 124, Mathematical Centrum, Amsterdam.

    Google Scholar 

  • Gill, R. D. (1983). Large sample behavior of the product limit estimator on the whole line,Ann. Statist.,11, 49–58.

    Google Scholar 

  • Jacod, J. (1975). Multivariate point processes: predicable projection, Radon-Nykodym derivatives, representation of martingales,Z. Wahrsch. verw. Gebiete,31, 235–253.

    Google Scholar 

  • Lipster, R. S. and Shiryayev, A. N. (1978).Statistics of Random Processes II: Applications, Springer, New York.

    Google Scholar 

  • Lo, A. Y. (1987). A large sample study of the Bayesian bootstrap,Ann. Statist.,15, 360–375.

    Google Scholar 

  • Lo, A. Y. (1988). A Bayesian bootstrap for a finite population,Ann. Statist.,16, 1684–1685.

    Google Scholar 

  • Lo, A. Y. (1993). A Bayesian bootstrap for censored data,Ann. Statist.,21, 100–123.

    Google Scholar 

  • Rebolledo, R. (1980). Central limit theorems for local martingales,Z. Wahrsch. verw. Gebiete,51, 269–289.

    Google Scholar 

  • Reid, N. (1981). Estimating the median survival time,Biometrika,68, 601–608.

    Google Scholar 

  • Rubin, D. B. (1981). The Bayesian bootstrap,Ann. Statist.,9, 130–134.

    Google Scholar 

  • Susarla, V. and Van Ryzin, J. (1976). Nonparametric Bayesian estimation of survival curves from incomplete data,J. Amer. Statist. Assoc.,71, 897–902.

    Google Scholar 

  • Susarla, V. and Van Ryzin, J. (1978). Large sample theory for a Bayesian nonparametric survival curve estimator based on censored samples,Ann. Statist.,6, 755–768.

    Google Scholar 

  • Weng, C. S. (1989). On a second order asymptotic property of the Bayesian bootstrap mean,Ann. Statist.,17, 705–710.

    Google Scholar 

  • Ying, Z. (1989). A note on the asymptotic properties of the product limit estimator on the whole line,Statist. Probab. Lett.,7, 311–314.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Wells, M.T., Tiwari, R.C. Bootstrapping a Bayes estimator of a survival function with censored data. Ann Inst Stat Math 46, 487–495 (1994). https://doi.org/10.1007/BF00773512

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00773512

Key words and phrases

Navigation