A note on wavelet regression with uniform random design and heteroscedastic errors

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

A nonparametric regression model with uniform random design and heteroscedastic errors (with a deterministic structure) is considered. The distributions of the errors are unknown; we only know that they admit finite moments of order $2$. Based on this general framework, we want to estimate the unknown regression function. To reach this goal, an adaptive nonlinear wavelet estimator is developed. Taking the minimax approach under the MISE over Besov balls, we prove that it attains a sharp rate of convergence, closed to the one attains by the optimal non-realistic linear wavelet estimator.

Mots clés: Regression; Heteroscedastic errors; Minimax estimation; Besov balls; Wavelets; Hard thresholding

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

Christophe Chesneau. A note on wavelet regression with uniform random design and heteroscedastic errors. 2010. ⟨hal-00449970v2⟩