Efficient estimation of analytic density under random censorship

E. Belitser

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    Abstract

    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.
    Original languageEnglish
    Pages (from-to)519-543
    Number of pages25
    JournalBernoulli
    Volume4
    Issue number4
    DOIs
    Publication statusPublished - 1998

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