On strong laws of large numbers for arrays of rowwise independent random elements

Abolghassem Bozorgnia, Ronald Frank Patterson and Robert Lee Taylor

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-5

Abstract:

Let { X n k } be an array of rowwise independent random elements in a separable Banach space of type r , 1 ≤ r ≤ 2 . Complete convergence of n 1 / p ∑ k = 1 n X n k to 0 , 0 < p < r ≤ 2 is obtained when sup 1 ≤ k ≤ n E   ‖ X n k ‖ v = O ( n α ) , α ≥ 0 with v ( 1 p − 1 r ) > α + 1 . An application to density estimation is also given.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:836452

DOI: 10.1155/S0161171293000729

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