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Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding

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  • Chen, Song Xi
  • Guo, Bin
  • Qiu, Yumou

Abstract

The paper considers testing and signal identification for covariance matrices from two populations of marginally sub-Gaussian distributed. A multi-level thresholding procedure is proposed for testing the equality of two high-dimensional covariance matrices, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic composition is developed to establish the asymptotic distribution of the thresholding statistics in conjunction with the matrix blocking and the coupling techniques. It is shown that the proposed test is more powerful than the existing tests in detecting sparse and weak signals in covariances. Multiple testing procedures are constructed to discover different covariances and the sub-groups of variables with different covariance structures between the two populations. The proposed procedures are based on the multi-level thresholding test, which are able to control the false discovery proportion (FDP) with high power. Simulation experiments and a case study on the returns of the S&P 500 stocks before and after the COVID-19 pandemic are conducted to demonstrate and compare the utilities of the proposed methods.

Suggested Citation

  • Chen, Song Xi & Guo, Bin & Qiu, Yumou, 2023. "Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding," Journal of Econometrics, Elsevier, vol. 235(2), pages 1337-1354.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1337-1354
    DOI: 10.1016/j.jeconom.2022.10.008
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    References listed on IDEAS

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    More about this item

    Keywords

    Detection boundary; High dimensionality; Multiple testing; Rare and faint signal; Thresholding;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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