Linear wavelet estimation of the derivatives of a regression function based on biased data

Yogendra P. Chaubey (1) , Christophe Chesneau (2) , Fabien Navarro (1)

1 Concordia University [Montreal]
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

This paper deals with the problem of estimating the derivatives of a regression function based on biased data. We develop two different linear wavelet estimators according to the knowledge of the "biased density" of the design. The new estimators are analyzed with respect to their $L_p$ risk with p ≥ 1 over Besov balls. Fast polynomial rates of convergence are obtained.

Mots clés: Besov balls; Wavelets; Biased data; Deriva-tives function estimation; Nonparametric regression

Domaines: Statistiques [math.ST]

Yogendra P. Chaubey, Christophe Chesneau, Fabien Navarro. Linear wavelet estimation of the derivatives of a regression function based on biased data. Communications in Statistics - Theory and Methods, 2017, 46 (19), ⟨10.1080/03610926.2016.1213287⟩. ⟨hal-01075544⟩