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

Alexander Dürre and Davy Paindaveine

Statistics & Probability Letters, 2023, vol. 193, issue C

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.

Keywords: Consistency; Convergence rates; Incomplete U-statistics; Moment assumptions (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2022.109714

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