Presmoothed kernel density estimator for censored data

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Abstract
Some kernel density estimator is presented in the context of right randomly censored data. The estimator makes use of presmoothing ideas replacing the indicators of no censoring by some preliminary nonparametric estimator of the conditional probability of uncensoring. Some i.i.d representation is given for this presmoothing estimator. This is useful to obtain the limit distribution and the asymptotic mean squared error of the estimator. An asymptotic mean integrated squared error result is also presented and used to derive large-sample formulas for the optimal presmoothing and the smoothing parameters. Finally, some simulations illustrate the theory.