Central Limit Theorems for Reduced U‐Statistics Under Dependence and Their Usefulness

Summary A reduced -statistic is a -statistic with its summands drawn from a restricted but balanced set of pairs. In this article, central limit theorems are derived for reduced -statistics under -mixing, which significantly extends the work of Brown & Kildea in various aspects. It will be shown and illustrated that reduced -statistics are quite useful in deriving test statistics in various nonparametric testing problems.