Adaptive wavelet regression in random design and general errors with weakly dependent data

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We investigate function estimation in a nonparametric regression model having the following particularities: the design is random (with a known distribution), the errors admit finite moments of order 2 and the data are weakly dependent; the exponentially strongly mixing case is considered. In this general framework, we construct a new adaptive estimator. It is based on wavelets and the combination of two hard thresholding rules. We determine an upper bound of the associated mean integrated squared error and prove that it is sharp for a wide class of regression functions.

Mots clés: Nonparametric regression; Weakly dependent data; Minimax estimation; Besov balls; Wavelets; Hard thresholding; Hard thresholding.

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

Christophe Chesneau. Adaptive wavelet regression in random design and general errors with weakly dependent data. 2011. ⟨hal-00562228⟩