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Simultaneous testing of the mean vector and covariance matrix among k populations for high-dimensional data

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  • Masashi Hyodo
  • Takahiro Nishiyama

Abstract

In this study, we propose an L2-norm-based test for simultaneous testing of the mean vector and covariance matrix for high-dimensional non-normal populations. We extend to k sample problems the procedures developed for two-sample problems by Hyodo and Nishiyama [Hyodo, M., Nishiyama, T., A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data, TEST]. To accomplish this, we derive an asymptotic distribution of a test statistic based on differences of both mean vectors and covariance matrices. We also investigate the asymptotic sizes and powers of the proposed tests using this result. Finally, we study the finite sample and dimension performance of this test through Monte Carlo simulations.

Suggested Citation

  • Masashi Hyodo & Takahiro Nishiyama, 2021. "Simultaneous testing of the mean vector and covariance matrix among k populations for high-dimensional data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(3), pages 663-684, February.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:3:p:663-684
    DOI: 10.1080/03610926.2019.1639751
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    Cited by:

    1. Mingxiang Cao & Yuanjing He, 2022. "A high-dimensional test on linear hypothesis of means under a low-dimensional factor model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 557-572, July.
    2. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    3. Fraiman, Ricardo & Moreno, Leonardo & Ransford, Thomas, 2023. "A Cramér–Wold theorem for elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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