On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator

Christophe Chesneau (1) , Fabien Navarro (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 CREST - Centre de Recherche en Economie et Statistique [Bruz]

In this paper we provide a theoretical contribution to the point-wise mean squared error of an adaptive multidimensional term-by-term thresholding wavelet estimator. A general result exhibiting fast rates of convergence under mild assumptions on the model is proved. It can be applied for a wide range of nonparametric models including possible dependent observations. We give applications of this result for the nonpara-metric regression function estimation problem (with random design) and the conditional density estimation problem.

Mots clés: Density estimation; and phrases: Pointwise mean squared error; Wavelet methods; Nonparametric regression

Domaines: Statistiques [math.ST]

Christophe Chesneau, Fabien Navarro. On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator. Communications in Statistics - Theory and Methods, 2017, 46 (11), ⟨10.1080/03610926.2015.1107587⟩. ⟨hal-01188362v3⟩