2021/12/29 by Alexander Dürre, Dürre, Alexander, Davy Paindaveine +1
Mathematics · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2112.14666
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.