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Article Dans Une Revue Mathematical Methods of Statistics Année : 2009

Adaptive density estimation for stationary processes

Résumé

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework.
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Dates et versions

hal-00413692 , version 1 (04-09-2009)

Identifiants

Citer

Matthieu Lerasle. Adaptive density estimation for stationary processes. Mathematical Methods of Statistics, 2009, 18 (1), pp.59--83. ⟨10.3103/S1066530709010049⟩. ⟨hal-00413692⟩
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