Adaptive density deconvolution with dependent inputs

Abstract : In the convolution model $Z_i=X_i+ \varepsilon_i$, we give a model selection procedure to estimate the density of the unobserved variables $(X_i)_{1 \leq i \leq n}$, when the sequence $(X_i)_{i \geq 1}$ is strictly stationary but not necessarily independent. This procedure depends on wether the density of $\varepsilon_i$ 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 ${\mathbb R}$. 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 $(X_i)_{i \geq 1}$ is not a long-memory process.
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Pré-publication, Document de travail
MAP5 2008-06. 2006
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https://hal.archives-ouvertes.fr/hal-00078865
Contributeur : Marie-Luce Taupin <>
Soumis le : mercredi 7 juin 2006 - 17:43:30
Dernière modification le : mercredi 4 janvier 2017 - 16:22:47
Document(s) archivé(s) le : lundi 5 avril 2010 - 22:28:14

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Fabienne Comte, Jérôme Dedecker, Marie-Luce Taupin. Adaptive density deconvolution with dependent inputs. MAP5 2008-06. 2006. <hal-00078865>

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