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

Robert Lee Taylor and Ronald Frank Patterson

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-10

Abstract:

Let { X n k , 1 ≤ k ≤ n , n ≤ 1 } be a triangular array of row-wise exchangeable random elements in a separable Banach space. The almost sure convergence of n − 1 / p ∑ k = 1 n X n k , 1 ≤ p < 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.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:863212

DOI: 10.1155/S0161171285000126

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