Central Limit Theorems for Reduced U‐Statistics Under Dependence and Their Usefulness |
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| Authors: | Tae Yoon Kim Jeongcheol Ha Sun Young Hwang Cheolyong Park Zhi‐Ming Luo |
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| Institution: | 1. Department of Statistics, Keimyung University, , Daegu, 704‐701 Korea;2. Department of Statistics, Sookmyung Women's University, , Seoul, 140–742 Korea |
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| Abstract: | 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. |
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| Keywords: | central limit theorem reduced ‐statistic ‐mixing nonparametric test |
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