We derive a consistency result, in the $L_1$-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 $p(\geq 1)$, we obtain a bound on the $L_1$ 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.

翻译：我们得出了一个一致结果,即在1美元标准值中,对于手头的内核有无限的二阶时的非标准案例中的不完整的U-统计,我们得出了一个一致的结果。假设内核有一定的点点数,我们得到的是在不完全的U-统计及其Dirac弱点之间的1美元距离上,这使我们能够为任何固定的1美元获得一致性率的上限。我们的结果维持了多数用于获得不完整的U-统计的典型抽样方案。