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Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices

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  • Qing Yang
  • Guangming Pan

Abstract

This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function of the population covariance matrix. The simulation results confirm that our statistic is powerful against all alternatives, while other tests given in the literature fail in at least one situation. Supplementary materials for this article are available online.

Suggested Citation

  • Qing Yang & Guangming Pan, 2017. "Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 188-200, January.
  • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:517:p:188-200
    DOI: 10.1080/01621459.2015.1122602
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    Cited by:

    1. Ping‐Shou Zhong, 2023. "Homogeneity tests of covariance for high‐dimensional functional data with applications to event segmentation," Biometrics, The International Biometric Society, vol. 79(4), pages 3332-3344, December.
    2. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).

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