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CENTRAL LIMIT THEOREMS FOR REDUCED U-STATISTICS UNDER DEPENDENCE AND THEIR USEFULNESS
- Issue Date
- Dec-2013
- Publisher
- WILEY-BLACKWELL
- Keywords
- α-mixing; Central limit theorem; Nonparametric test; Reduced U-statistic
- Citation
- AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, v.55, no.4, pp 387 - 399
- Pages
- 13
- Journal Title
- AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS
- Volume
- 55
- Number
- 4
- Start Page
- 387
- End Page
- 399
- ISSN
- 1369-1473
1467-842X
- Abstract
- 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.
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