| Article ID: | iaor201524992 |
| Volume: | 55 |
| Issue: | 4 |
| Start Page Number: | 387 |
| End Page Number: | 399 |
| Publication Date: | Dec 2013 |
| Journal: | Australian & New Zealand Journal of Statistics |
| Authors: | Kim Tae Yoon, Ha Jeongcheol, Hwang Sun Young, Park Cheolyong, Luo Zhi-Ming |
| Keywords: | central limit theorem |
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.