International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 587-591
doi:10.1155/S0161171293000729
On strong laws of large numbers for arrays of rowwise independent random elements
Abolghassem Bozorgnia1
, Ronald Frank Patterson2
and Robert Lee Taylor3
1Department of Statistics, Mashhad University, Mashhad, Iran
2Department of Mathematics and Computer Science, Georgia State University, Atlanta 30303, Ga, USA
3Department of Statistics, University of Georgia, Athens 30602, Ga, USA
Abstract
Let {Xnk} be an array of rowwise independent random elements in a separable Banach space of type r, 1≤r≤2. Complete convergence of n1/p∑k=1nXnk to 0, 0<p<r≤2 is obtained when sup1≤k≤nE ‖Xnk‖v=O(nα), α≥0 with v(1p−1r)>α+1. An application to density estimation is also given.