Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions

Peng Sun; Yincai Tang; Mingxiang Cao

doi:10.3390/math10224339

Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.

Original language	English
Article number	4339
Journal	Mathematics
Volume	10
Issue number	22
DOIs	https://doi.org/10.3390/math10224339
State	Published - Nov 2022

Keywords

asymptotic distributions
high-dimensional data
homogeneity test
martingale central limit theorem
weighted Frobenius norm

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10.3390/math10224339

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title = "Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions",

abstract = "In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.",

keywords = "asymptotic distributions, high-dimensional data, homogeneity test, martingale central limit theorem, weighted Frobenius norm",

author = "Peng Sun and Yincai Tang and Mingxiang Cao",

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year = "2022",

month = nov,

doi = "10.3390/math10224339",

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AU - Sun, Peng

AU - Tang, Yincai

AU - Cao, Mingxiang

PY - 2022/11

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N2 - In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.

AB - In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.

KW - asymptotic distributions

KW - high-dimensional data

KW - homogeneity test

KW - martingale central limit theorem

KW - weighted Frobenius norm

UR - https://www.scopus.com/pages/publications/85142503467

U2 - 10.3390/math10224339

DO - 10.3390/math10224339

M3 - 文章

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VL - 10

JO - Mathematics

JF - Mathematics

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Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions

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Keywords

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