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Limit theorems for triangular arrays under a relaxed asymptotic negligibility condition
Published online by Cambridge University Press: 09 April 2009
Abstract
Let {Xnk} be a triangular array of independent random variables satisfying the so-called tail-negligibility condition, i.e. such that Prob{|Xnk| > a} → 0 as both k, n → ∞. It is also assumed that for each fixed k, Xnk converges in distribution as n → ∞. Theorems on the asymptotic behavior of the row sums of the array, analogous to those of the classical theory under the uniform negligibility condition, are presented.
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- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 42 , Issue 1 , February 1987 , pp. 117 - 128
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- Copyright © Australian Mathematical Society 1987
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