Censored data arises when whole life span of an event cannot be observed due to early termination, only partial life time is recorded. This type of data is widely encountered in real life. How to estimate the density of life span as if the density of censors is given? A nonparametric density estimator based on shrinkage adaptation is proposed. Because the underlying density of censors is unknown, Kaplan-Meier estimator is used to find censoring distribution. It is assumed that the underlying density belongs to Sobolev space. The estimator is adaptive in the sense that it adapts to unknown smoothness of underlying density of lifetimes. The estimator achieves both optimal convergent rate and sharp constant. The estimator is studied through both theory and simulations.
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