Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 271303, 7 pages
http://dx.doi.org/10.1155/2014/271303
Research Article

A Note on the Adaptive Estimation of a Multiplicative Separable Regression Function

Laboratoire de Mathématiques Nicolas Oresme, Université de Caen Basse-Normandie, Campus II, Science 3, 14032 Caen, France

Received 18 January 2014; Accepted 25 February 2014; Published 20 March 2014

Academic Editors: F. Ding, E. Skubalska-Rafajlowicz, and H. C. So

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.

Abstract

We investigate the estimation of a multiplicative separable regression function from a bidimensional nonparametric regression model with random design. We present a general estimator for this problem and study its mean integrated squared error (MISE) properties. A wavelet version of this estimator is developed. In some situations, we prove that it attains the standard unidimensional rate of convergence under the MISE over Besov balls.