Christophe Chesneau, Fabien Navarro, Oana Silvia Serea
A note on the adaptive estimation of the differential entropy by wavelet methods

Comment.Math.Univ.Carolin. 58,1 (2017) 87-100.

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.

Keywords: entropy; wavelet estimation; rate of convergence; mean $\mathbb{L}_p$ error

DOI: DOI 10.14712/1213-7243.2015.191
AMS Subject Classification: 62G07 62G20