Nonparametric Estimation for Functional Data by Wavelet Thresholding

Christophe Chesneau (1) , Maher Kachour (2) , Bertrand Maillot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 LMJL - Laboratoire de Mathématiques Jean Leray

This paper deals with density and regression estimation problems for functional data. Using wavelet bases for Hilbert spaces of functions, we develop a new adaptive procedure based on wavelet thresholding. We provide theoretical results on its asymptotic performances.

Mots clés: Hard thresholding.; Functional data; Density estimation; Nonparametric regression; Wavelets; Hard thresholding

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

Christophe Chesneau, Maher Kachour, Bertrand Maillot. Nonparametric Estimation for Functional Data by Wavelet Thresholding. REVSTAT - Statistical Journal, 2013, 11 (2), pp.211--230. ⟨hal-00634800v2⟩