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 Ahmed1
, T.-C. Hu2
and Andrei I. Volodin1
1Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Saskatchewan, Canada
2a University, Hsinchu 300, Taiwan
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.