A CRAMER MODERATE DEVIATION THEOREM FOR HOTELLING'S T2-STATISTIC WITH APPLICATIONS TO GLOBAL TESTS

• 成果类型: Article
• 署名作者: Liu, Weidong; Shao, Qi-Man
• 署名单位: Shanghai Jiao Tong University; Chinese University of Hong Kong
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1082
• 发表日期: 2013
• 页码: 296-322
• 关键词: higher criticism; students-t; shape; approximations

摘要

A Cramer moderate deviation theorem for Hotelling's T-2-statistic is proved under a finite (3 + delta)th moment. The result is applied to large scale tests on the equality of mean vectors and is shown that the number of tests can be as large as e(0)(n(1/3)) before the chi-squared distribution calibration becomes inaccurate. As an application of the moderate deviation results, a global test on the equality of m mean vectors based on the maximum of Hotelling's T-2-statistics is developed and its asymptotic null distribution is shown to be an extreme value type I distribution. A novel intermediate approximation to the null distribution is proposed to improve the slow convergence rate of the extreme distribution approximation. Numerical studies show that the new test procedure works well even for a small sample size and performs favorably in analyzing a breast cancer dataset.