A note on adaptive wavelet estimation in a shifted curves model via block thresholding

Christophe Chesneau (1) , Jalal M. Fadili (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 Equipe Image - Laboratoire GREYC - UMR6072

In this paper, the problem of adaptive estimation of a mean pattern in a randomly shifted curve model is considered. Adopting the new point of view of Bigot and Gadat (2008), we develop an adaptive estimator based on wavelet block thresholding. Taking the minimax approach, we prove that it attains near optimal rates of convergence under the quadratic risk over a wide range of Besov balls. In comparison to the procedure of Bigot and Gadat (2008), we gain a logarithmic term in the rates of convergence (for the regular zone).

Mots clés: Mean pattern estimation; Deconvolution; Adaptive curve estimation; Wavelets; Block thresholding

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

Christophe Chesneau, Jalal M. Fadili. A note on adaptive wavelet estimation in a shifted curves model via block thresholding. 2009. ⟨hal-00421743⟩