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A unified approach to testing mean vectors with large dimensions

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  • M. Rauf Ahmad

    (Uppsala University)

Abstract

A unified testing framework is presented for large-dimensional mean vectors of one or several populations which may be non-normal with unequal covariance matrices. Beginning with one-sample case, the construction of tests, underlying assumptions and asymptotic theory, is systematically extended to multi-sample case. Tests are defined in terms of U-statistics-based consistent estimators, and their limits are derived under a few mild assumptions. Accuracy of the tests is shown through simulations. Real data applications, including a five-sample unbalanced MANOVA analysis on count data, are also given.

Suggested Citation

  • M. Rauf Ahmad, 2019. "A unified approach to testing mean vectors with large dimensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 593-618, December.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:4:d:10.1007_s10182-018-00343-z
    DOI: 10.1007/s10182-018-00343-z
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    References listed on IDEAS

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    1. Shota Katayama & Yutaka Kano, 2014. "A New Test on High-Dimensional Mean Vector Without Any Assumption on Population Covariance Matrix," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(24), pages 5290-5304, December.
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    6. Makoto Aoshima & Kazuyoshi Yata, 2015. "Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 419-439, June.
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    8. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    9. M. Ahmad, 2014. "A $$U$$ -statistic approach for a high-dimensional two-sample mean testing problem under non-normality and Behrens–Fisher setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 33-61, February.
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    Cited by:

    1. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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