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The weak law of large numbers for arrays

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  • Gut, Allan

Abstract

The laws of large numbers for sums of i.i.d. random variables can be generalized in various ways. The purpose of this note is to collect some domination conditions and to provide a fairly general weak law for arrays. AMS 1980 Subject Classifications: Primary: 60F05, 60F25, 60G42, 60G50

Suggested Citation

  • Gut, Allan, 1992. "The weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 49-52, May.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:1:p:49-52
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    Cited by:

    1. Clément de Chaisemartin & Luc Behaghel, 2020. "Estimating the Effect of Treatments Allocated by Randomized Waiting Lists," Econometrica, Econometric Society, vol. 88(4), pages 1453-1477, July.
    2. Cl'ement de Chaisemartin & Diego Ciccia Xavier D'Haultf{oe}uille & Felix Knau, 2024. "Two-way Fixed Effects and Differences-in-Differences Estimators in Heterogeneous Adoption Designs," Papers 2405.04465, arXiv.org, revised Aug 2024.
    3. Gut, Allan & Stadtmüller, Ulrich, 2017. "Strong laws for sequences in the vicinity of the LIL," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 63-72.
    4. Hu, Tien-Chung & Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 155-164, January.
    5. Adler, André & Rosalsky, Andrew & Volodin, Andrej I., 1997. "A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 167-174, March.
    6. Sung, Soo Hak & Hu, Tien-Chung & Volodin, Andrei, 2005. "On the weak laws for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 291-298, May.
    7. Hong, Dug Hun, 1996. "On the weak law of large numbers for randomly indexed partial sums for arrays," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 127-130, June.
    8. Christofides, Tasos C. & Serfling, Robert, 1998. "U-statistics on a lattice of I.I.D. random variables," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 293-303, October.
    9. Ankirchner, Stefan & Kruse, Thomas & Urusov, Mikhail, 2017. "WLLN for arrays of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 73-78.
    10. Sung, Soo Hak, 1998. "Weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 101-105, June.
    11. Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "On conditional compactly uniform pth-order integrability of random elements in Banach spaces," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 301-309, December.
    12. Sung, Soo Hak, 1999. "Weak law of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 293-298, April.
    13. Hong, Dug Hun & Cabrera, Manuel Ordóñez & Sung, Soo Hak & Volodin, Andrei I., 2000. "On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 177-185, January.

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