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The Marcinkiewicz–Zygmund law of large numbers for exchangeable arrays

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  • Davezies, Laurent
  • D’Haultfœuille, Xavier
  • Guyonvarch, Yannick

Abstract

We show a Marcinkiewicz–Zygmund law of large numbers for jointly, dissociated exchangeable arrays, in Lr (r∈(0,2)) and almost surely. Then, we obtain a law of iterated logarithm for such arrays under a weaker moment condition than the existing one.

Suggested Citation

  • Davezies, Laurent & D’Haultfœuille, Xavier & Guyonvarch, Yannick, 2022. "The Marcinkiewicz–Zygmund law of large numbers for exchangeable arrays," Statistics & Probability Letters, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:stapro:v:188:y:2022:i:c:s0167715222001031
    DOI: 10.1016/j.spl.2022.109536
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    References listed on IDEAS

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    1. Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    2. Henry Teicher, 1998. "On the Marcinkiewicz–Zygmund Strong Law for U-Statistics," Journal of Theoretical Probability, Springer, vol. 11(1), pages 279-288, January.
    3. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
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