Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 543723, 12 pages
Research Article

Tightness Criterion and Weak Convergence for the Generalized Empirical Process in

Department of Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38d, 20-618 Lublin, Poland

Received 27 June 2013; Accepted 23 August 2013

Academic Editors: M. Campanino, S. Lototsky, H. J. Paarsch, and L. Sacerdote

Copyright © 2013 Maciej Ziemba. 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.


We prove Shao and Yu's tightness criterion for the generalized empirical process in the space with topology. Covariance inequalities are used in applying the criterion to particular types of the empirical processes. We weaken the assumptions imposed on the covariance structure as well as the properties of the underlying sequence of r.v.'s, under which presented processes converge weakly.