International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 10, Pages 629-635

On the rate of convergence of bootstrapped means in a Banach space

S. Ejaz Ahmed,1 T.-C. Hu,2 and Andrei I. Volodin1

1Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Saskatchewan, Canada
2Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan

Received 5 January 2000; Revised 5 May 2000

Copyright © 2001 S. Ejaz Ahmed et al. 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 establish the complete convergence for arrays of Banach space valued random elements. This result is applied to bootstrapped means of random elements to obtain their strong consistency and is derived in the spirit of Baum-Katz/Hsu-Robbins/Spitzer type convergence.