2003 Prépublication d'Orsay numéro 2003-60 (20/10/2003)



ADAPTIVE DENSITY DECONVOLUTION FOR CIRCULAR DATA.

COMTE, Fabienne - MAP5 (Statistique) Université René Descartes, 45,rue des Saints-Pères 75270 Paris cedex 06
TAUPIN, Marie-Luce - Modélisation Stochastique et Statistique, Université Paris-Sud, Bât. 425, 91405 Orsay cedex


Mots Clés : Absolutely regular random variables.Adaptive estimation. Circular variables.Density deconvolution. Model selection.Penalized contrast estimator.

Classification MSC : 62G07


Resumé :

Abstract :
We consider the problem of density deconvolution in the context of circular random variable. We aim at estimating the density of a random variable $X$ from a sample $Z_1,\cdots, Z_n$ in the convolution model where $Z_i=X_i+\varepsilon_i$, $i=1, \dots, n$ and $\varepsilon$ is a noise independent of $X$, all the variables being defined on $\mathbb{R}$-modulo $2\pi$. In this context, we propose an adaptive estimator of the density of $X$ by using a model selection procedure allowing to find non-asymptotic bounds for the integrated quadratic risk. These bounds hold in the independent case as well as in the dependent case.

Article : Fichier Postscript
Contact : marie-luce.taupin@math.u-psud.fr