International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 604150, 21 pages
doi:10.1155/2011/604150
Research Article

Adaptive Wavelet Estimation of a Biased Density for Strongly Mixing Sequences

Université de Caen-Basse Normandie, Département de Mathématiques, UFR de Sciences, 14032 Caen, France

Received 7 December 2010; Accepted 24 February 2011

Academic Editor: Palle E. Jorgensen

Copyright © 2011 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

The estimation of a biased density for exponentially strongly mixing sequences is investigated. We construct a new adaptive wavelet estimator based on a hard thresholding rule. We determine a sharp upper bound of the associated mean integrated square error for a wide class of functions.