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On the consistency of incomplete U-statistics under infinite second-order moments

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  • Dürre, Alexander
  • Paindaveine, Davy

Abstract

We derive a consistency result, in the L1-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order p(≥1), we obtain a bound on the L1 distance between the incomplete U-statistic and its Dirac weak limit, which allows us to obtain, for any fixed p, an upper bound on the consistency rate. Our results hold for most classical sampling schemes that are used to obtain incomplete U-statistics.

Suggested Citation

  • Dürre, Alexander & Paindaveine, Davy, 2023. "On the consistency of incomplete U-statistics under infinite second-order moments," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002279
    DOI: 10.1016/j.spl.2022.109714
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    References listed on IDEAS

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    1. 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.
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