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A more powerful test of equality of high-dimensional two-sample means

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  • Zhang, Huaiyu
  • Wang, Haiyan

Abstract

A new test is proposed for testing the equality of two sample means in high dimensional data in which the sample sizes may be much less than the dimension. The test is constructed based on a studentized average of squared component-wise t-statistics. Asymptotic normality of the test statistic was derived under H0. Theoretical properties of the power function were given under local alternatives. The new test has much better type I error control and power compared to a similarly constructed competing test in recent literature as a result of a more efficient scaling parameter estimate in the test statistic. Monte Carlo experiments show that the new test outperforms several popular competing tests under various data settings, especially when components of the data vector have high correlations. The results are established under the condition that there exists a permutation of the component indices such that the correlation decays suitably fast (at least with polynomial rate). The test is further evaluated with a real-data task of identifying differently expressed Gene Ontology terms with the acute lymphoblastic leukemia gene expression data. The new test provides more consistent results on random samples of the dataset.

Suggested Citation

  • Zhang, Huaiyu & Wang, Haiyan, 2021. "A more powerful test of equality of high-dimensional two-sample means," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:csdana:v:164:y:2021:i:c:s0167947321001523
    DOI: 10.1016/j.csda.2021.107318
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    References listed on IDEAS

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    Cited by:

    1. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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