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

Christophe Chesneau (1) , Fabien Navarro (2) , Oana Silvia Serea (3)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CREST - Centre de Recherche en Economie et Statistique [Bruz]
3 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

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

Domaines: Statistiques [math.ST]

Christophe Chesneau, Fabien Navarro, Oana Silvia Serea. A note on the adaptive estimation of the differential entropy by wavelet methods. Commentationes Mathematicae Universitatis Carolinae, 2017, 58 (1), ⟨10.14712/1213-7243.2015.191⟩. ⟨hal-01141420v3⟩