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Strong law of large numbers for 2-exchangeable random variables

Author

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  • Etemadi, N.
  • Kaminski, M.

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.

Suggested Citation

  • Etemadi, N. & Kaminski, M., 1996. "Strong law of large numbers for 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 245-250, July.
    • Handle: RePEc:eee:stapro:v:28:y:1996:i:3:p:245-250
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    References listed on IDEAS

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    1. Robertson, James B. & Womack, James M., 1985. "A pairwise independent stationary stochastic process," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 195-199, July.
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    Cited by:

    1. Etemadi, N., 2007. "Stability of weighted averages of 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 389-395, February.
    2. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2010. "Limit Theorems for Empirical Processes Based on Dependent Data," Quaderni di Dipartimento 132, University of Pavia, Department of Economics and Quantitative Methods.
    3. Etemadi, N., 1997. "Criteria for the strong law of large numbers for sequences of arbitrary random vectors," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 151-157, April.
    4. Etemadi, N., 1999. "Maximal inequalities for averages of i.i.d. and 2-exchangeable random variables," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 195-200, August.
    5. Terán, Pedro, 2008. "On a uniform law of large numbers for random sets and subdifferentials of random functions," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 42-49, January.

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