International Journal of Mathematics and Mathematical Sciences 
Volume 25 (2001), Issue 10, Pages 629-635
doi:10.1155/S0161171201005191

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

Abstract

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.