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

Christophe Chesneau; Fabien Navarro; Oana Silvia Serea — 2017

Commentationes Mathematicae Universitatis Carolinae

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, $p \geq 1$ , this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical findings.

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