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Abstract and Applied Analysis
Volume 2014, Article ID 143581, 5 pages
Research Article

Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process

1College of Mathematics and Information, Henan University, Kaifeng 475000, China
2Department of Economics, Zhengzhou Institute of Finance and Economics, Zhengzhou 450000, China

Received 10 May 2014; Accepted 21 July 2014; Published 27 August 2014

Academic Editor: Ahmed El-Sayed

Copyright © 2014 Junshan Xie and Lin He. 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.


Let be a sequence of iid U[0, 1]-distributed random variables, and define the uniform empirical process , . When the nonnegative function satisfies some regular monotone conditions, it proves that .