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

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