AISM 53, 289-306
© 2001 ISM

Asymptotically local minimax estimation of infinitely smooth density with censored data

Eduard Belitser1 and Boris Levit2

1Department of Mathematics, Vrije Universiteit, de Boelelaan 1081a, 1081 HV Amsterdam, the Netherlands
2Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, the Netherlands

(Received February 9, 1998; revised September 28, 1999)

Abstract.    The problem of the nonparametric minimax estimation of an infinitely smooth density at a given point, under random censorship, is considered. We establish the exact asymptotics of the local minimax risk and propose the efficient kernel-type estimator based on the well known Kaplan-Meier estimator.

Key words and phrases:    Efficient estimator, local minimax risk, Kaplan-Meier estimator, kernel, random censorship.

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