Efficient estimation of analytic density under random censorship

E. Belitser

    Research output: Contribution to journalArticleAcademicpeer-review

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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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    Random Censorship
    Efficient Estimation
    Minimax Risk
    Minimax Estimation
    Minimax Estimator
    Kaplan-Meier Estimator
    Limiting Behavior
    Nonparametric Estimation
    Censoring
    Irregular
    kernel

    Cite this

    Belitser, E. / Efficient estimation of analytic density under random censorship. In: Bernoulli. 1998 ; Vol. 4, No. 4. pp. 519-543.
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    Efficient estimation of analytic density under random censorship. / Belitser, E.

    In: Bernoulli, Vol. 4, No. 4, 1998, p. 519-543.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AB - 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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