WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
A Novel Test for the Homogeneity of Several Covariance Matrices in High-Dimensional Data: Application to Gene Expression Analysis
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Abstract: This paper introduces a new test for the homogeneity of several covariance matrices in high-dimensional data under the p-variate normal distribution. The test is constructed using U-statistic-based estimators to evaluate differences among covariance matrices, and applies an inverse-variance-weighted method to quantify the relative importance of these estimators. Its distribution under the null hypothesis is derived and follows a chi-square distribution as the dimension and sample sizes increase. Simulation results indicate that the test controls the Type I error rate better than three existing methods and achieves high power. To demonstrate its practical applicability, two real gene-expression datasets involving three- and four-group comparisons are analyzed.
Keywords:
Multivariate normal distribution, homogeneity test, covariance matrices, U-statistics, empirical Type I error rate, empirical power, autoregressive structure, gene expression data
Pages: 36-50
DOI: 10.37394/23206.2026.25.5