Discusses shrinkage estimation in nonparametric Bayesian survival analysis using censored data. The shrinkage estimators proposed are based on estimating the parameter measure of a prior Dirichlet process in a nonparametric Bayesian survival curve estimator which is the posterior mean of this process. The shrinkage is toward a prior family of exponential survival curves. The estimators are then compared by simulation with the wholly nonparametric estimator of Kaplan-Meier and the maximum likelihood estimator for the exponential family. These comparisons are done in cases where the exponential assumption is both correct and incorrect. The simulation comparisons are by three distance norms and for four levels of censoring and two or four sample sizes. Generally speaking, the shrinkage estimator which is mean squared consistent, is shown to be better than the Kaplan-Meier estimator with the improvement increasing dramatically as the censoring percentage increases.
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