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On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality

Author

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  • Niu, Zhenzhen
  • Hu, Jiang
  • Bai, Zhidong
  • Gao, Wei

Abstract

In this paper, we primarily focus on simultaneous testing mean vector and covariance matrix with high-dimensional non-Gaussian data, based on the classical likelihood ratio test. Applying the central limit theorem for linear spectral statistics of sample covariance matrices, we establish new modification for the likelihood ratio test, and find that this modified test converges in distribution to normal distribution, when the dimension p tends to infinity, proportionate to the sample size n under the null hypothesis. Furthermore, we conduct a simulation study to examine the performance of the test and compare it with other tests proposed in past studies. As the simulation results show, our empirical powers are clearly superior to those of other tests in a series of settings.

Suggested Citation

  • Niu, Zhenzhen & Hu, Jiang & Bai, Zhidong & Gao, Wei, 2019. "On LR simultaneous test of high-dimensional mean vector and covariance matrix under non-normality," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 338-344.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:338-344
    DOI: 10.1016/j.spl.2018.10.008
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    References listed on IDEAS

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    1. 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.
    2. Tiefeng Jiang & Yongcheng Qi, 2015. "Likelihood Ratio Tests for High-Dimensional Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 988-1009, December.
    3. Srivastava, Muni S. & Du, Meng, 2008. "A test for the mean vector with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 386-402, March.
    4. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
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