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Central Limit Theorems for Reduced U ‐Statistics Under Dependence and Their Usefulness
Author(s) -
Kim Tae Yoon,
Ha Jeongcheol,
Hwang Sun Young,
Park Cheolyong,
Luo ZhiMing
Publication year - 2013
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12045
Subject(s) - mathematics , statistic , nonparametric statistics , limit (mathematics) , central limit theorem , statistics , mixing (physics) , statistical hypothesis testing , set (abstract data type) , mathematical analysis , physics , quantum mechanics , computer science , programming language
Summary A reduced U ‐statistic is a U ‐statistic with its summands drawn from a restricted but balanced set of pairs. In this article, central limit theorems are derived for reduced U ‐statistics under α ‐mixing, which significantly extends the work of Brown & Kildea in various aspects. It will be shown and illustrated that reduced U ‐statistics are quite useful in deriving test statistics in various nonparametric testing problems.