International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 135-144
Strong laws of large numbers for arrays of row-wise exchangeable random elements
1Department of Statistics and Computer Science, University of Georgia, Athens 30602, GA, USA
2Department of Mathematics, Georgia State University, Atlanta 30303, GA, USA
Received 1 October 1984
Copyright © 1985 Robert Lee Taylor and Ronald Frank Patterson. 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.
Let be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of , is obtained under varying moment and distribution conditions on the random elements. In particular, strong laws of large numbers follow for triangular arrays of random elements in(Rademacher) type separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.