Subsampling based inference for U statistics under thick tails using self-normalization

We consider a subsampling approach for U-statistics based on a self-normalized statistic recently suggested by Shao (2015) and establish its consistency. A simple finite averaging of the self-normalizer is proposed to reduce the average length of the associated confidence interval. Our procedure is robust to thick tailed distributions and skewed distributions and in simulations for the Gini index, is seen to provide an improvement over the t-statistic based intervals.