Table of Contents
ISRN Probability and Statistics
Volume 2014, Article ID 864530, 7 pages
http://dx.doi.org/10.1155/2014/864530
Research Article

Average Derivative Estimation from Biased Data

1Département de Mathématiques, UFR de Sciences, LMNO, Université de Caen Basse-Normandie, 14032 Caen Cedex, France
2École Supérieure de Commerce IDRAC, 47 rue Sergent Michel Berthet CP 607, 69258 Lyon Cedex 09, France
3Laboratoire de Mathématiques Jean Leray, UFR Sciences et Techniques, Université de Nantes, 2 rue de la Houssiniére, BP 92208, F-44322 Nantes Cedex 3, France

Received 18 January 2014; Accepted 15 February 2014; Published 11 March 2014

Academic Editors: N. W. Hengartner, O. Pons, C. A. Tudor, and Y. Wu

Copyright © 2014 Christophe Chesneau et al. 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.

Abstract

We investigate the estimation of the density-weighted average derivative from biased data. An estimator integrating a plug-in approach and wavelet projections is constructed. We prove that it attains the parametric rate of convergence under the mean squared error.