Test for high dimensional covariance matrices

Han, Yuefeng; Wu, Wei Biao

doi:10.1214/20-aos1943

Cited by 3 publications

(2 citation statements)

References 46 publications

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“…First, a general multivariate model is applied to obtain asymptotic results. Although it is a common assumption in the literature, it would be useful to investigate the asymptotic properties of our proposed method in weaker conditions, for example, assumption 2.1 in Han and Wu (2020). Second, we consider a two-sample test for high-dimensional covariance matrices.…”

Section: Discussionmentioning

confidence: 99%

Use of Random Integration to Test Equality of High Dimensional Covariance Matrices

Jiang¹,

Wen²,

Jiang³

et al. 2024

STAT SINICA

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Testing the equality of two covariance matrices is a fundamental problem in statistics, and especially challenging when the data are high-dimensional. Through a novel use of random integration, we can test the equality of high-dimensional covariance matrices without assuming parametric distributions for the two underlying populations, even if the dimension is much larger than the sample size. The asymptotic properties of our test for arbitrary number of covariates and sample size are studied in depth under a general multivariate model. The finite-sample performance of our test is evaluated through numerical studies. The empirical results demonstrate that our test is highly competitive with existing tests in a wide range of settings. In particular, our proposed test is distinctly powerful under different settings when there exist a few large or many small diagonal disturbances between the two covariance matrices.

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Section: Discussionmentioning

confidence: 99%

Use of Random Integration to Test Equality of High Dimensional Covariance Matrices

Jiang¹,

Wen²,

Jiang³

et al. 2024

STAT SINICA

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show abstract

“…Through a novel application of random integration, Jiang et al (2023) developed a powerful test under various settings, especially when there are a few large or many small diagonal disturbances between the two covariance matrices. See more about Frobenius norm based tests, for example, Li and Chen (2012), Chen et al (2010), Qiu and Chen (2012), Zhong et al (2017) and Han and Wu (2020). The other class of test statistics is based on maximum norm.…”

Section: Introductionmentioning

confidence: 99%

Double verification for two‐sample covariance matrices test

Sun,

Lyu,

Guo

2024

Stat

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This paper explores testing the equality of two covariance matrices under high‐dimensional settings. Existing test statistics are usually constructed based on the squared Frobenius norm or the elementwise maximum norm. However, the former may experience power loss when handling sparse alternatives, while the latter may have a poor performance against dense alternatives. In this paper, with a novel framework, we introduce a double verification test statistic designed to be powerful against both dense and sparse alternatives. Additionally, we propose an adaptive weight test statistic to enhance power. Furthermore, we present an analysis of the asymptotic size and power of the proposed test. Simulation results demonstrate the satisfactory performance of our proposed method.

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Testing for independence in high dimensions based on empirical copulas

Bücher,

Pakzad

2024

Ann. Statist.

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Test for high dimensional covariance matrices

Cited by 3 publications

References 46 publications

Use of Random Integration to Test Equality of High Dimensional Covariance Matrices

Use of Random Integration to Test Equality of High Dimensional Covariance Matrices

Double verification for two‐sample covariance matrices test

Testing for independence in high dimensions based on empirical copulas

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