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Consistency of the kernel density estimator - a survey

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  • Wied, Dominik
  • Weißbach, Rafael
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    Abstract

    Various consistency proofs for the kernel density estimator have been developed over the last few decades. Important milestones are the pointwise consistency and almost sure uniform convergence with a fixed bandwidth on the one hand and the rate of convergence with a fixed or even a variable bandwidth on the other hand. While considering global properties of the empirical distribution functions is sufficient for strong consistency, proofs of exact convergence rates use deeper information about the underlying empirical processes. A unifying character, however, is that earlier and more recent proofs use bounds on the probability that a sum of random variables deviates from its mean. --

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    File URL: http://econstor.eu/bitstream/10419/39692/1/tr03-09.pdf
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    Bibliographic Info

    Article provided by ZBW - German National Library of Economics in its journal EconStor Open Access Articles.

    Volume (Year): (2010)
    Issue (Month): ()
    Pages: 1-21

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    Handle: RePEc:zbw:espost:39692

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    Related research

    Keywords: Kernel estimation; Pointwise consistency; Strong uniform consistency; Empirical process; Rate of convergence; Variable bandwidth;

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    1. Diehl, Sabine & Stute, Winfried, 1988. "Kernel density and hazard function estimation in the presence of censoring," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 299-310, May.
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    Cited by:
    1. Dutta, Santanu & Goswami, Alok, 2013. "Pointwise and uniform convergence of kernel density estimators using random bandwidths," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2711-2720.

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