Test of the Equality of Several High-Dimensional Covariance Matrices: A Normal-Reference Approach

Jingyi Wang, Tianming Zhu () and Jin-Ting Zhang
Additional contact information
Jingyi Wang: Department of Statistics and Data Science, National University of Singapore, Singapore 117546, Singapore
Tianming Zhu: National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore
Jin-Ting Zhang: Department of Statistics and Data Science, National University of Singapore, Singapore 117546, Singapore

Mathematics, 2025, vol. 13, issue 2, 1-22

Abstract: As the field of big data continues to evolve, there is an increasing necessity to evaluate the equality of multiple high-dimensional covariance matrices. Many existing methods rely on approximations to the null distribution of the test statistic or its extreme-value distributions under stringent conditions, leading to outcomes that are either overly permissive or excessively cautious. Consequently, these methods often lack robustness when applied to real-world data, as verifying the required assumptions can be arduous. In response to these challenges, we introduce a novel test statistic utilizing the normal-reference approach. We demonstrate that the null distribution of this test statistic shares the same limiting distribution as a chi-square-type mixture under certain regularity conditions, with the latter reliably estimable from data using the three-cumulant matched chi-square-approximation. Additionally, we establish the asymptotic power of our proposed test. Through comprehensive simulation studies and real data analysis, our proposed test demonstrates superior performance in terms of size control compared to several competing methods.

Keywords: k-sample equal-covariance matrix testing; chi-square-type mixtures; high-dimensional data; three-cumulant matched chi-square-approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/2/295/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/2/295/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:2:p:295-:d:1569694

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().