Adaptive wavelet deconvolution for strongly mixing sequences

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

This paper studies the estimation of a density in the convolution density model from weakly dependent observations. The ordinary smooth case is considered. Adopting the minimax approach under the mean integrated square error over Besov balls, we explore the performances of two wavelet estimators: a standard linear one based on projections and a new non-linear one based on a hard thresholding rule. In particular, under strong mixing conditions, we prove that our hard thresholding estimator attains a particular rate of convergence: the optimal one in the {\it i.i.d.} case up to a logarithmic term.

Mots clés: Deconvolution; Strongly mixing; Adaptivity; Wavelets; Hard thresholding

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Christophe Chesneau. Adaptive wavelet deconvolution for strongly mixing sequences. 2011. ⟨hal-00569957⟩