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Article Dans Une Revue Mathematical Methods of Statistics Année : 2014

Adaptive density deconvolution with dependent inputs

Résumé

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.

Dates et versions

hal-04432167 , version 1 (01-02-2024)

Identifiants

Citer

Fabienne Comte, Jérôme Dedecker, Marie-Luce L Taupin. Adaptive density deconvolution with dependent inputs. Mathematical Methods of Statistics, 2014, 17 (2), pp.87. ⟨10.3103/S1066530708020014⟩. ⟨hal-04432167⟩
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