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Consistency of the kernel density estimator - a survey

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  • Wied, Dominik
  • Weißbach, Rafael

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.

Suggested Citation

  • Wied, Dominik & Weißbach, Rafael, 2010. "Consistency of the kernel density estimator - a survey," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 53(1), pages 1-21.
    • Handle: RePEc:zbw:espost:39692
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    References listed on IDEAS

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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.
    2. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.
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    Cited by:

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    2. R. Zamini & V. Fakoor & M. Sarmad, 2015. "On estimation of a density function in multiplicative censoring," Statistical Papers, Springer, vol. 56(3), pages 661-676, August.
    3. 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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