International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1985 / Article

Open Access

Volume 8 |Article ID 863212 | https://doi.org/10.1155/S0161171285000126

Robert Lee Taylor, Ronald Frank Patterson, "Strong laws of large numbers for arrays of row-wise exchangeable random elements", International Journal of Mathematics and Mathematical Sciences, vol. 8, Article ID 863212, 10 pages, 1985. https://doi.org/10.1155/S0161171285000126

Strong laws of large numbers for arrays of row-wise exchangeable random elements

Received01 Oct 1984

Abstract

Let {Xnk,1kn,n1} be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n1/pk=1nXnk,1p<2, 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 p separable Banach spaces. Consistency of the kernel density estimates can be obtained in this setting.

Copyright © 1985 Hindawi Publishing Corporation. 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.


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