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Divergence-type errors of smooth Barron-type density estimators

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Abstract

Barron-type estimators are histogram-based distribution estimators that have been proved to have good consistency properties according to several information theoretic criteria. However they are not continuous. In this paper, we examine a new class of continuous distribution estimators obtained as a combination of Barron-type estimators with the frequency polygon. We prove the consistency of these estimators in expected information divergence and expected χ2-divergence. For one of then we evaluate the rate of convergence in expected χ2-divergence.

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Authors and Affiliations

  1. Department of Mathematics, Section of Applied Mathematics, Catholic University Leuven, Belgium

    Jan Beirlant

  2. Laboratory of Probability and Statistics, University Montpellier II, France

    Alain Berlinet & Gérard Biau

  3. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Czech Republic

    Igor Vajda

Authors
  1. Jan Beirlant
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  2. Alain Berlinet
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  3. Gérard Biau
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  4. Igor Vajda
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Corresponding author

Correspondence to Gérard Biau.

Additional information

Jan Beirlant is supported by the University Montpellier II. Igor Vajda is supported by the GACR grant 102/99/1137 and by the University Montpellier II.

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Beirlant, J., Berlinet, A., Biau, G. et al. Divergence-type errors of smooth Barron-type density estimators. Test 11, 191–217 (2002). https://doi.org/10.1007/BF02595736

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  • DOI: https://doi.org/10.1007/BF02595736

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