Geodesic
A note on the adaptive estimation of the differential entropy by wavelet methods
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 87-100.

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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 $\mathbb{L}_p$ 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.
DOI : 10.14712/1213-7243.2015.191
Classification : 62G07, 62G20
Keywords: entropy; wavelet estimation; rate of convergence; mean $\mathbb{L}_p$ error 
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Chesneau, Christophe; Navarro, Fabien; Serea, Oana Silvia. A note on the adaptive estimation  of the differential entropy by wavelet methods. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 87-100. doi : 10.14712/1213-7243.2015.191. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.191/

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