Open Access
Dec 1998 Efficient estimation of analytic density under random censorship
Eduard Belitser
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Bernoulli 4(4): 519-543 (Dec 1998).


The nonparametric minimax estimation of an analytic density at a given point, under random censorship, is considered. Although the problem of estimating density is known to be irregular in a certain sense, we make some connections relating this problem to the problem of estimating smooth functionals. Under condition that the censoring is not too severe, we establish the exact limiting behaviour of the local minimax risk and propose the efficient (locally asymptotically minimax) estimator - an integral of some kernel with respect to the Kaplan-Meier estimator.


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Eduard Belitser. "Efficient estimation of analytic density under random censorship." Bernoulli 4 (4) 519 - 543, Dec 1998.


Published: Dec 1998
First available in Project Euclid: 14 March 2007

zbMATH: 1037.62025
MathSciNet: MR1679796

Keywords: asymptotic local minimax risk , Density estimation , Kaplan-Meier estimator , ‎kernel‎ , random censorship

Rights: Copyright © 1998 Bernoulli Society for Mathematical Statistics and Probability

Vol.4 • No. 4 • Dec 1998
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