Abstract
This paper proposes procedures for testing the equality hypothesis and the proportionality hypothesis involving a large number of q covariance matrices of dimension p × p. Under a limiting scheme where p, q and the sample sizes from the q populations grow to infinity in a proper manner, the proposed test statistics are shown to be asymptotically normal. Simulation results show that finite sample properties of the test procedures are satisfactory under both the null and alternatives. As an application, we derive a test procedure for the Kronecker product covariance specification for transposable data. Empirical analysis of datasets from the Mouse Aging Project and the 1000 Genomes Project (phase 3) is also conducted.
| Original language | English |
|---|---|
| Pages (from-to) | 4039-4074 |
| Number of pages | 36 |
| Journal | Electronic Journal of Statistics |
| Volume | 18 |
| Issue number | 2 |
| Early online date | 18 Oct 2024 |
| DOIs | |
| Publication status | Published - 2024 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024, Institute of Mathematical Statistics. All rights reserved.
Funding
Chen Wang was partially supported by Hong Kong RGC General Research Fund 17301021 and National Natural Science Foundation of China Grant 72033002. Jianfeng Yao was partially supported by NSFC RFIS Grant No. 12350710179.
Keywords
- equality hypothesis
- hypothesis testing
- large co-variance matrix
- Many-sample test
- multivariate analysis
- proportionality hypothesis
- transposable data
- U-statistics