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On the adaptive wavelet estimation of a multidimensional regression function under α -mixing dependence: Beyond the standard assumptions on the noise

Christophe Chesneau — 2013

Commentationes Mathematicae Universitatis Carolinae

We investigate the estimation of a multidimensional regression function f from n observations of an α -mixing process ( Y , X ) , where Y = f ( X ) + ξ , X represents the design and ξ the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of f in its construction) or it is supposed that ξ is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....

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

Christophe ChesneauFabien NavarroOana 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 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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