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.
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References
Akritas, M. G. (1986). Bootstrapping the Kaplan-Meier estimator,J. Amer. Statist. Assoc.,81, 1032–1038.
Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.
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.
Efron, B. (1981). Censored data and the bootstrap,J. Amer. Statist. Assoc.,76, 312–319.
Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems,Ann. Statist.,1, 209–230.
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.
Gill, R. D. (1983). Large sample behavior of the product limit estimator on the whole line,Ann. Statist.,11, 49–58.
Jacod, J. (1975). Multivariate point processes: predicable projection, Radon-Nykodym derivatives, representation of martingales,Z. Wahrsch. verw. Gebiete,31, 235–253.
Lipster, R. S. and Shiryayev, A. N. (1978).Statistics of Random Processes II: Applications, Springer, New York.
Lo, A. Y. (1987). A large sample study of the Bayesian bootstrap,Ann. Statist.,15, 360–375.
Lo, A. Y. (1988). A Bayesian bootstrap for a finite population,Ann. Statist.,16, 1684–1685.
Lo, A. Y. (1993). A Bayesian bootstrap for censored data,Ann. Statist.,21, 100–123.
Rebolledo, R. (1980). Central limit theorems for local martingales,Z. Wahrsch. verw. Gebiete,51, 269–289.
Reid, N. (1981). Estimating the median survival time,Biometrika,68, 601–608.
Rubin, D. B. (1981). The Bayesian bootstrap,Ann. Statist.,9, 130–134.
Susarla, V. and Van Ryzin, J. (1976). Nonparametric Bayesian estimation of survival curves from incomplete data,J. Amer. Statist. Assoc.,71, 897–902.
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.
Weng, C. S. (1989). On a second order asymptotic property of the Bayesian bootstrap mean,Ann. Statist.,17, 705–710.
Ying, Z. (1989). A note on the asymptotic properties of the product limit estimator on the whole line,Statist. Probab. Lett.,7, 311–314.
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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
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DOI: https://doi.org/10.1007/BF00773512