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Testing the equality of two high‐dimensional spatial sign covariance matrices
Author(s) -
Cheng Guanghui,
Liu Baisen,
Peng Liuhua,
Zhang Baoxue,
Zheng Shurong
Publication year - 2019
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12350
Subject(s) - mathematics , covariance function , covariance , test statistic , sign (mathematics) , null distribution , estimation of covariance matrices , covariance matrix , matérn covariance function , norm (philosophy) , asymptotic distribution , dimension (graph theory) , statistical hypothesis testing , statistics , combinatorics , mathematical analysis , covariance intersection , law , estimator , political science
This paper is concerned with testing the equality of two high‐dimensional spatial sign covariance matrices with applications to testing the proportionality of two high‐dimensional covariance matrices. It is interesting that these two testing problems are completely equivalent for the class of elliptically symmetric distributions. This paper develops a new test for testing the equality of two high‐dimensional spatial sign covariance matrices based on the Frobenius norm of the difference between two spatial sign covariance matrices. The asymptotic normality of the proposed testing statistic is derived under the null and alternative hypotheses when the dimension and sample sizes both tend to infinity. Moreover, the asymptotic power function is also presented. Simulation studies show that the proposed test performs very well in a wide range of settings and can be allowed for the case of large dimensions and small sample sizes.