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-deficiency of the Kaplan-Meier estimator

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  • Lemdani, Mohamed
  • Ould-Saïd, Elias

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.

Suggested Citation

  • Lemdani, Mohamed & Ould-Saïd, Elias, 2003. "-deficiency of the Kaplan-Meier estimator," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 145-155, June.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:2:p:145-155
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    References listed on IDEAS

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    1. M. Falk, 1983. "Relative efficiency and deficiency of kernel type estimators of smooth distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 37(2), pages 73-83, June.
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