Testing diagonality of high-dimensional covariance matrix under non-normality

Xu, Kai

doi:10.1080/00949655.2017.1362405

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…Yang and Pan (2015) extend the canonical correlation through regularization for high-dimensional case. Another test, using block correlation matrices, is proposed in Bao et al (2017), where Srivastava, Kollo, and von Rosen (2011) and Xu (2017) provide diagonality tests relaxing normality assumption, where a similarity coefficient based treatment is given in Ahmad (2019).…”

Section: Introductionmentioning

confidence: 99%

Some correlation tests for vectors of large dimension

Ahmad

Ahmed

2021

Communications in Statistics - Theory and Methods

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For a random sample of n iid p-dimensional vectors, each partitioned into b sub-vectors of dimensions p i , i ¼ 1, :::, b, tests for zero correlation of sub-vectors are presented when p i ) n and the distribution need not be normal. The test statistics are composed of U-statistics based estimators of the Frobenius norm measuring the distance between the null and alternative hypotheses. Asymptotic distributions of the tests are provided for n, p i ! 1, with their finite-sample performance demonstrated through simulations. Some related tests are discussed. A real data application is also given.

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Section: Introductionmentioning

confidence: 99%

Some correlation tests for vectors of large dimension

Ahmad

Ahmed

2021

Communications in Statistics - Theory and Methods

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“…This estimator is unbiased under the normality population assumption, but is biased for the non-normal case. Some studies indicate that the test procedures which work well under the normality assumption may encounter performance degradation when the population dispenses with the normality assumption (see for example [4,5]). Therefore, for the test problem (1) under the non-normal case, Srivastava et al [6] modified the test statistic in [1] by providing an unbiased estimator of 2 tr i  for general models; Ahmad [7] constructed the test statistic based on the U -statistics with the additional assumption of zero mean vectors.…”

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confidence: 99%

Testing homogeneity of high-dimensional covariance matrices under non-normality

Shen

2022

J. Phys.: Conf. Ser.

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In this paper, we test the homogeneity of multiple covariance matrices when the dimension may exceed the sample sizes. A test statistic is proposed which does not depend on the normality assumption. Furthermore, the asymptotic distribution of the test statistic is derived. Numerical simulations indicate that the proposed test has accurate significance level, and has a greater improvement in power than some existing tests.

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