The authors consider the problem of estimating the density g of independent and identically distributed variables X i , from a sample 21,. . . , 2, such that 2; = Xi + QE; for i = 1,. . . , n, and E is noise independent of X, with QE having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method. Deconvolution adaptative de densite par contraste penaliseRbumt! : Les auteurs considkrent le probltme de dkonvolution, c'est-&-dire de I'estimation de la densitt de variables altatoires identiquement distributes X,, ii partir de I'observation de Zi, oh 2; = X , + QE, pour i = 1,. . . , n, et oh les erreurs QE; sont de densit6 connue. Par une proc6dure de selection de modtles qui permet d'obtenir des bornes de risque non asymptotiques, ils construisent un estimateur adaptatif de la densitt des X ; . L'estimateur atteint automatiquement la vitesse minimax dans la plupart des cas, que les erreurs ou la densit6 & estimer soient peu ou trhs dgulitres. Une ttude par simulation illustre les bonnes performances pratiques de la mtthode.

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In the convolution model Zi = Xi + εi, we give a model selection procedure to estimate the density of the unobserved variables (Xi) 1≤i≤n , when the sequence (Xi) i≥1 is strictly stationary but not necessarily independent. This procedure depends on wether the density of εi is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most classes of regularity on R. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are super smooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence (Xi) i≥1 is not a long-memory process.MSC 2000 Subject Classifications. 62G07-62G20