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On adaptive wavelet estimation of a class of weighted densities

Fabien Navarro 1, 2, Christophe Chesneau 1, Jalal Fadili 2

(2012-07-04)

We investigate the estimation of a weighted density taking the form $g=w(F)f$, where $f$ denotes an unknown density, $F$ the associated distribution function and $w$ is a known (non-negative) weight. Such a class encompasses many examples, including those arising in order statistics or when $g$ is related to the maximum or the minimum of $N$ (random or fixed) independent and identically distributed (\iid) random variables. We here construct a new adaptive non-parametric estimator for $g$ based on a plug-in approach and the wavelets methodology. For a wide class of models, we prove that it attains fast rates of convergence under the $\mathbb{L}_p$ risk with $p\ge 1$ (not only for $p = 2$ corresponding to the mean integrated squared error) over Besov balls. The theoretical findings are illustrated through several simulations.

1:	Laboratoire de Mathématiques Nicolas Oresme (LMNO)
	CNRS : UMR6139 – Université de Caen Basse-Normandie
2:	Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC)
	CNRS : UMR6072 – Université de Caen Basse-Normandie – Ecole Nationale Supérieure d'Ingénieurs de Caen

Research team: image

Subject

:

Mathematics/Statistics Statistics/Statistics Theory

Keyword(s): Weighted density – density estimation – plug-in approach – wavelets – block thresholding – reliability – series system – parallel system.

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From: Fabien Navarro <>

Submitted on: Wednesday, 4 July 2012 18:27:25

Updated on: Wednesday, 4 July 2012 19:15:23