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The law of the large numbers for U-statistics for 2m-wise independent random variables

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  • Arcones, Miguel A.

Abstract

The strong law of the large numbers for U-statistics has been proved for a sequence of independent random variables using martingale techniques. We see that the condition of independence can be relaxed to 2m-wise independence. In this case martingale techniques cannot be applied. We also consider Marcinkiewicz laws of large numbers for U-statistics for a special case.

Suggested Citation

  • Arcones, Miguel A., 1998. "The law of the large numbers for U-statistics for 2m-wise independent random variables," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 75-81, September.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:1:p:75-81
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    Cited by:

    1. Dehling, Herold G. & Sharipov, Olimjon Sh., 2009. "Marcinkiewicz-Zygmund strong laws for U-statistics of weakly dependent observations," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2028-2036, October.

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