A STUDY ON KERNEL ESTIMATION OF A SMOOTH DISTRIBUTION FUNCTION ON CENSORED DATA

  • Jee, Eun Sook (Department of mathematics, Kwang Woon University)
  • Published : 1992.12.01

Abstract

The problem of estimating a smooth distribution function F at a point $\tau$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($\tau$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($\tau$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.

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