Journal of Mathematics and Statistics

Complete Convergence of Exchangeable Sequences

George Stoica

DOI : 10.3844/jmssp.2011.95.97

Journal of Mathematics and Statistics

Volume 7, Issue 2

Pages 95-97

Abstract

We prove that exchangeable sequences converge completely in the Baum-Katz sense under the same conditions as i.i.d. sequences do. Problem statement: The research was needed as the rate of convergence in the law of large numbers for exchangeable sequences was previously obtained under restricted hypotheses. Approach: We applied powerful techniques involving inequalities for independent sequences of random variables. Results: We obtained the maximal rate of convergence and provided an example to show that our findings are sharp. Conclusion/Recommendations: The technique used in the paper may be adapted in the similar study for identically distributed sequences.

Copyright

© 2011 George Stoica. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.