Mathematics and Statistics Vol. 12(5), pp. 455 - 464
DOI: 10.13189/ms.2024.120507
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A New Test for Equality of Two Covariance Matrices in High-Dimensional Data

Saowapa Chaipitak ¹, Boonyarit Choopradit ^2,*
1 Department of Statistics, Faculty of Science, Kasetsart University, Thailand
² Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Thailand

ABSTRACT

High-dimensional data, characterized by datasets with many variables (dimension) relative to the number of observations, is growing in prominence owing to advances in data collection and storage capabilities. This data type is widespread across various fields. While it presents unique challenges and opportunities, robust statistical approaches are crucial for effectively leveraging the potential of high-dimensional data. In multivariate statistical analysis, the likelihood ratio test (LRT) is frequently used for evaluating the equality of two covariance matrices. Nevertheless, the LRT lacks definition in high-dimensional data contexts. This paper aims to introduce a new test for ascertaining the equality of two covariance matrices in high-dimensional data, especially for datasets that follow a multivariate normal distribution. The test () proposed in this study utilizes consistent estimators in quadratic and symmetric bilinear forms. As the dimension and sample sizes approach infinity, the asymptotic null distribution of the test converges to the standard normal distribution. A simulation study was conducted to assess the performance of the proposed test compared to three existing tests. The existing tests were proposed by Schott in 2007, Srivastava and Yanagihara in 2010, and Li and Chen in 2012. The focus was on type I error rates and the test's power under spherical and Toeplitz covariance matrix structures. The simulation results demonstrate that outperforms the tests proposed by Srivastava and Yanagihara, as well as Li and Chen, in all scenarios evaluated. Moreover, it performs comparably to Schott's test. Additionally, demonstrates remarkable stability even when faced with alterations in the covariance matrix structure. This robust performance of suggests that it can serve as a reliable tool for statistical inference in multivariate analyses, especially in high-dimensional contexts. For practitioners, the use of the proposed test could mean more accurate decision-making in scientific research and policymaking, where precision and reliability are paramount.

KEYWORDS
Multivariate Normal Distribution, High-dimensional Covariance Matrix, DNA Microarray Data, Toeplitz Structure, Spherical Structure

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Saowapa Chaipitak , Boonyarit Choopradit , "A New Test for Equality of Two Covariance Matrices in High-Dimensional Data," Mathematics and Statistics, Vol. 12, No. 5, pp. 455 - 464, 2024. DOI: 10.13189/ms.2024.120507.

(b). APA Format:
Saowapa Chaipitak , Boonyarit Choopradit (2024). A New Test for Equality of Two Covariance Matrices in High-Dimensional Data. Mathematics and Statistics, 12(5), 455 - 464. DOI: 10.13189/ms.2024.120507.