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-deficiency of the Kaplan-Meier estimator

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Abstract

Let X1,...,Xn,... be a sequence of independent and identically distributed random variables with distribution function F subject to random right censoring. Considering the classical Kaplan-Meier estimator and a smoothed kernel-type estimate , we prove that and (mean integrated absolute error) tend to the same constant as n goes to infinity. However, we establish that the smoothed estimator has a performance better than (for some bandwidths) what relative -deficiency is of interest. The optimal choice of the bandwidth hn, with respect to MIAE sense, is also obtained.

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