A general result on the performance of the wavelet hard thresholding estimator under $\alpha$-mixing dependence

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

In this note, we consider the estimation of an unknown function $f$ for weakly dependent data ($\alpha$-mixing) in a general setting. Our contribution is theoretical: we prove that a wavelet hard thresholding estimator attains a sharp rate of convergence under the mean integrated squared error (MISE) over Besov balls without imposing too restrictive assumptions on the model. Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. Another application concerns the regression model with random design.

Mots clés: Nonparametric statistics; alpha-mixing dependence; wavelets; hard thresholding

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

Christophe Chesneau. A general result on the performance of the wavelet hard thresholding estimator under $\alpha$-mixing dependence. 2014. ⟨hal-00809862v3⟩