Test on the linear combinations of covariance matrices in high-dimensional data

  • Zhidong Bai
  • Jiang HuEmail author
  • Chen Wang
  • Chao Zhang
Regular Article


In this paper, we propose a new test on the linear combinations of covariance matrices in high-dimensional data. Our statistic can be applied to many hypothesis tests on covariance matrices. In particular, the test proposed by Li and Chen (Ann Stat 40:908–940, 2012) on the homogeneity of two population covariance matrices is a special case of our test. The results are illustrated by an empirical example in financial portfolio allocation.


Multi-sample test Covariance matrices U-statistic CLT 

Mathematics Subject Classification

Primary 62H15 Secondary 62E20 



The authors would like to thank the associate editor and two anonymous referees, whose comments improve the quality of the paper significantly. The research was partially supported by NSFC (No. 11571067, 11771073), Foundation of Jilin Educational Committee (No. JJKH20190288KJ), the Fundamental Research Funds for the Central Universities and The University of Hong Kong Start-up Fund.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.KLASMOE and School of Mathematics and StatisticsNortheast Normal UniversityChangchunChina
  2. 2.Department of Statistics and Actuarial ScienceUniversity of Hong KongPokfulamHong Kong

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