Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 264217, 9 pages
http://dx.doi.org/10.1155/2014/264217
Research Article

Superoptimal Rate of Convergence in Nonparametric Estimation for Functional Valued Processes

LMNO, CNRS, Université de Caen, Campus II, Science 3, 14032 Caen, France

Received 5 March 2014; Revised 12 May 2014; Accepted 4 June 2014; Published 16 September 2014

Academic Editor: Armelle Guillou

Copyright © 2014 Christophe Chesneau and Bertrand Maillot. 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 consider the nonparametric estimation of the generalised regression function for continuous time processes with irregular paths when the regressor takes values in a semimetric space. We establish the mean-square convergence of our estimator with the same superoptimal rate as when the regressor is real valued.