On the domain of attraction of a Tracy-Widom law with applications to testing multiple largest roots

JOURNAL OF MULTIVARIATE ANALYSIS

卷:165

Article

Chetelat, Didier¹  Narayanan, Rajendran²  Wells, Martin T.³ 

[1] Ecole Polytech Montreal, Dept Math & Genie Ind, Montreal, PQ, Canada

[2] Azim Premji Univ, Sch Liberal Studies, Bengaluru, India

[3] Cornell Univ, Dept Stat Sci, Ithaca, NY 14853 USA

关键词: Characteristic root;    Equality of covariance matrices;    Greatest root statistic;    Gumbel distribution;    MANOVA;    Multiple testing;    Multiway data;    Tracy-Widom laws;    Union-intersection test;   

DOI  :  10.1016/j.jmva.2017.11.008

来源: Elsevier

【 摘 要 】

The greatest root statistic arises as a test statistic in several multivariate analysis settings. Suppose there is a global null hypothesis H-0 that consists of m different independent sub null hypotheses, i.e., H-0 = H-01 boolean AND .... boolean AND H-0m and suppose the greatest root statistic is used as the test statistic for each sub null hypothesis. Such problems may arise when conducting a batch MANOVA or several batches of pairwise testing for equality of covariance matrices. Using the union-intersection testing approach, and by letting the problem dimension p -> infinity faster than m -> infinity, we show that H-0 can be tested using a Gumbel distribution to approximate the critical values. Although the theoretical results are asymptotic, simulation studies indicate that the approximation is accurate even for small to moderate dimensions. The results are general and can be applied in any setting where the greatest root statistic is used, not just for the two methods discussed for illustrative purposes. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free