A note on the adaptive estimation of the differential entropy by wavelet methods

Christophe Chesneau; Fabien Navarro; Oana Silvia Serea

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 1, page 87-100
  • ISSN: 0010-2628

Abstract

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In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean 𝕃 p 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 findings.

How to cite

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Chesneau, Christophe, Navarro, Fabien, and Serea, Oana Silvia. "A note on the adaptive estimation of the differential entropy by wavelet methods." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 87-100. <http://eudml.org/doc/287873>.

@article{Chesneau2017,
abstract = {In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean $\mathbb \{L\}_p$ error, $p\ge 1$, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.},
author = {Chesneau, Christophe, Navarro, Fabien, Serea, Oana Silvia},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {entropy; wavelet estimation; rate of convergence; mean $\mathbb \{L\}_p$ error},
language = {eng},
number = {1},
pages = {87-100},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on the adaptive estimation of the differential entropy by wavelet methods},
url = {http://eudml.org/doc/287873},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Chesneau, Christophe
AU - Navarro, Fabien
AU - Serea, Oana Silvia
TI - A note on the adaptive estimation of the differential entropy by wavelet methods
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 87
EP - 100
AB - In this note we consider the estimation of the differential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean $\mathbb {L}_p$ error, $p\ge 1$, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.
LA - eng
KW - entropy; wavelet estimation; rate of convergence; mean $\mathbb {L}_p$ error
UR - http://eudml.org/doc/287873
ER -

References

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