Central Limit Theorems for Reduced U‐Statistics Under Dependence and Their Usefulness. (11th October 2013)

• Record Type: Journal Article
• Authors: Kim, Tae Yoon; Ha, Jeongcheol; Hwang, Sun Young; Park, Cheolyong; Luo, Zhi‐Ming
• Is Part Of: Australian & New Zealand journal of statistics. Volume 55:Number 4(2013:Dec.)
• Page Start: 387
• Page End: 399
• Publication Date: 2013-10-11
• Subjects: Statistics -- Periodicals; 519.5
• DOI: 10.1111/anzs.12045
• Languages: English
• ISSNs: 1369-1473

Abstract

<abstract abstract-type="main" id="anzs12045-abs-0001"> <title>Summary</title> <p>A reduced <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg40crksk8" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:13691473:media:anzs12045:anzs12045-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math></alternatives>‐statistic is a <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg40crktj7" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:13691473:media:anzs12045:anzs12045-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math></alternatives>‐statistic with its summands drawn from a restricted but balanced set of pairs. In this article, central limit theorems are derived for reduced <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg40crktnw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:13691473:media:anzs12045:anzs12045-math-0005" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math></alternatives>‐statistics under <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg40crktfk" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:13691473:media:anzs12045:anzs12045-math-0006" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="italic">α</mml:mi></mml:math></alternatives>‐mixing, which significantly extends the work of Brown & Kildea in various aspects. It will be shown and illustrated that reduced <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg40crkthp" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:13691473:media:anzs12045:anzs12045-math-0007" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math></alternatives>‐statistics are quite useful in deriving test statistics in various nonparametric testing problems.</p> </abstract>