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New tests for the identity and sphericity of high-dimensional covariance matrices via U-statistics

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  • Xiong, Xiaoge

Abstract

Two novel test procedures are proposed for the identity and sphericity of covariance matrices in high-dimensional asymptotic frameworks, both constructed via U-statistics. The limiting distributions of these tests are established under null and local alternative hypotheses. Monte Carlo simulation results demonstrate their superiority over several competing methods across various scenarios, with the proposed tests achieving full power against both dense and sparse alternatives. The effectiveness of the proposed tests is further validated through an application to a colon dataset.

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  • Xiong, Xiaoge, 2025. "New tests for the identity and sphericity of high-dimensional covariance matrices via U-statistics," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:csdana:v:212:y:2025:i:c:s0167947325001185
    DOI: 10.1016/j.csda.2025.108242
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