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Strong law of large numbers for weighted U-statistics: Application to incomplete U-statistics

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  • Nasari, Masoud M.

Abstract

In this exposition we investigate almost sure convergence for weighted U-statistics. This strong law of large numbers is established for a class of divergent series of non-negative weights when the product of the kernel of the underlying weighted U-statistics and its logarithm is integrable. This result is used to establish the almost sure validity of incomplete U-statistics. Also, a method of constructing incomplete U-statistics of order 2 is introduced and its almost sure validity is established.

Suggested Citation

  • Nasari, Masoud M., 2012. "Strong law of large numbers for weighted U-statistics: Application to incomplete U-statistics," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1208-1217.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1208-1217
    DOI: 10.1016/j.spl.2012.03.010
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    Cited by:

    1. Dürre, Alexander & Paindaveine, Davy, 2023. "On the consistency of incomplete U-statistics under infinite second-order moments," Statistics & Probability Letters, Elsevier, vol. 193(C).
    2. Csörgő, Miklós & Nasari, Masoud M., 2013. "Asymptotics of randomly weighted u- and v-statistics: Application to bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 176-192.

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