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Consistency of the kernel density estimator: a survey

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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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Authors and Affiliations

  1. Institut für Wirtschafts- und Sozialstatistik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Dominik Wied

  2. Lehrstuhl für Statistik, Institut für Volkswirtschaftslehre, Universität Rostock, 18051, Rostock, Germany

    Rafael Weißbach

Authors
  1. Dominik Wied
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  2. Rafael Weißbach
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Correspondence to Dominik Wied.

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Wied, D., Weißbach, R. Consistency of the kernel density estimator: a survey. Stat Papers 53, 1–21 (2012). https://doi.org/10.1007/s00362-010-0338-1

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  • DOI: https://doi.org/10.1007/s00362-010-0338-1

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