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Finite sample penalization in adaptive density deconvolution

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We consider the problem of estimating the density g of identically distributed variables Xi, from a sample Z1, …, Zn, where Zi=Xi+εi, i=1, …, n and εi is a noise independent of Xi with known density -1fε(·/). We numerically study the adaptive estimators, constructed by a model selection procedure described by Comte et al. [2006, Penalized contrast estimator for density deconvolution, Canadian Journal of Statistics, 37(3)]. We illustrate their properties in various contexts and test their robustness (misspecification of errors, dependency and so on). Comparisons are made with respect to deconvolution kernel estimators. It appears that our estimation algorithm, based on a fast procedure, performs very well in all contexts.
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Keywords: Adaptive estimation; Data driven; Density deconvolution; Model selection; Penalized contrast; Projection estimator; Simulation study

Document Type: Research Article

Affiliations: 1: Université Paris V, Paris, France 2: Laboratoire de Probabilités, Statistique et Modélisation, IUT de Paris V et Université d'Orsay, Paris, France

Publication date: 01 January 2007

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