BOOTSTRAPPING A BAYES ESTIMATOR OF A SURVIVAL FUNCTION WITH CENSORED DATA

MARTIN T. WELLS^{1} AND RAM C. TIWARI^{2}

1Statistics Center, Cornell University, Ithaca, NY 14851, U.S.A. 2Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC 28223, U.S.A.

(Received February 8, 1993; revised December 27, 1993)

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.

Key words and phrases: Bayesian bootstrap, survival function, square-inte-grable martingales.