Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 569547, 10 pages
http://dx.doi.org/10.5402/2012/569547
Research Article

The Rate of Strong Consistency of the Nearest Neighbor Density Estimator for Negatively Dependent Random Variables

College of Science, Guilin University of Technology, Guilin 541004, China

Received 8 October 2012; Accepted 23 October 2012

Academic Editors: A. Bellouquid, J. A. Ferreira, and C. Lu

Copyright © 2012 Xiang Zeng and Qunying Wu. 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

Let be a sequence of negatively dependent random variables. Based on , in this paper we investigate the rate of pointwise consistency and strong consistency of the nonparametric density estimator proposed by Yu. We extend the correspondent results under the negatively dependent samples.