A pointwise Bayes-type estimator of the survival probability with censored data

In this note we propose an estimator of the survival function at a given time point using a Bayesian argument, an approach different from that of [Susarla, V., Van Ryzin, J., 1976. Nonparametric Bayesian estimation of survival curves from incomplete observations, Journal of the American Statistical Association 61, 897-902]. It is shown that the Kaplan-Meier (K-M) estimator is a special case of the proposed estimators. We show pointwise asymptotic normality of the proposed estimator for suitable choices of prior distributions.