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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 541250, 9 pages
http://dx.doi.org/10.1155/2013/541250
Research Article

A Berry-Esseen Type Bound in Kernel Density Estimation for Negatively Associated Censored Data

1College of Science, Guilin University of Technology, Guilin 541004, China
2Department of Mathematics, Ji'nan University, Guangzhou 510630, China

Received 19 February 2013; Accepted 11 July 2013

Academic Editor: XianHua Tang

Copyright © 2013 Qunying Wu and Pingyan Chen. 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 discuss the kernel estimation of a density function based on censored data when the survival and the censoring times form the stationary negatively associated (NA) sequences. Under certain regularity conditions, the Berry-Esseen type bounds are derived for the kernel density estimator and the Kaplan-Meier kernel density estimator at a fixed point .