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A note on the adaptive estimation of the di?erential entropy by wavelet methods

Author

Listed:
  • Christophe Chesneau

    (Université de Caen; LMNO)

  • Fabien Navarro

    (CREST;ENSAI)

  • Oana Silvia Serea

    (Université Perpignan; Laboratoire de Mathématiques et Physique)

Abstract

In this note we consider the estimation of the di?erential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean Lp error, p = 1, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical ?ndings.

Suggested Citation

  • Christophe Chesneau & Fabien Navarro & Oana Silvia Serea, 2017. "A note on the adaptive estimation of the di?erential entropy by wavelet methods," Working Papers 2017-69, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-69
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    References listed on IDEAS

    as
    1. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
    2. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
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    Keywords

    Entropy; Wavelet estimation; Rate of convergence; Mean Lp error;
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