Jackknife Empirical Likelihood for Infinite-Order U -Statistics

Infinite-order U -statistics play a vital role in modern statistics. However, given their degree k n kₙ k Subscript n depends on the sample size n , quantifying their variability is quite challenging, as fixed-degree theories cannot be directly adopted. In this article, we propose a jackknife empirical likelihood (EL) framework that can be used to construct confidence intervals for an infinite-order U -statistic. We establish sufficient conditions for the limiting chi-squared distribution of the JEL ratio statistic and introduce an efficient partition-sampling realization for practical implementation. To evaluate the performance of the proposed methodology, we conduct simulation studies in the context of subsampling-based ensemble methods and the maximum test, respectively, comparing its performance with four competing methods. The simulation studies yield satisfactory results across the board. Finally, we demonstrate the practical application of our method using a United States Forest Service timber auctions dataset to predict the highest bid at an auction.