Strong law of large numbers for 2-exchangeable random variables

N. Etemadi and M. Kaminski

Statistics & Probability Letters, 1996, vol. 28, issue 3, 245-250

Abstract: The investigation of the role of independence in the classical SLLN leads to a natural generalization of the SLLN to the case where the random variables are 2-exchangeable; namely, let {Xi: i [greater-or-equal, slanted] 1} be a sequence of random variables such that all ordered pairs (Xi, Xj), i [not equal to] j, are identically distributed. Then we show, among other things, that where X is in general a non-degenerate random variable. This provids a unified treatment of the SLLN for both exchangeable and pairwise independent random variables. We also show that, under 2-exchangeability, to preserve the Glivenko-Cantelli Theorem - sometimes refered to as the fundamental theorem of statistics - it is necessary that the random variables be pairwise independent.

Keywords: Exchangeable; 2-exchangeable; Pairwise; independent; Strong; Law (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (5)

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