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International Journal of Mathematics and Mathematical Sciences
Volume 2014, Article ID 195765, 8 pages
Research Article

A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting

Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, BP 5186, 14032 Caen Cedex, France

Received 8 January 2014; Accepted 11 March 2014; Published 3 April 2014

Academic Editor: A. Zayed

Copyright © 2014 Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of unknown functions.