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

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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. We prove that it attains fast rates of convergence under the mean Lp error, p ≥ 1, for a wide class of functions. A key result in our development is a new upper bound for the mean Lp error, p ≥ 1, of a general version of the plug-in estimator. This upper bound may be of independent interest.

Mots clés: and phrases: Entropy; Wavelet estimation; Rates of conver-gence; Mean Lp error

Domaines: Statistiques [math.ST]

Christophe Chesneau. A note on the adaptive estimation of the differential entropy by wavelet methods. 2015. ⟨hal-01141420v1⟩