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Power computation for hypothesis testing with high-dimensional covariance matrices

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  • Lin, Ruitao
  • Liu, Zhongying
  • Zheng, Shurong
  • Yin, Guosheng

Abstract

Based on the random matrix theory, a unified numerical approach is developed for power calculation in the general framework of hypothesis testing with high-dimensional covariance matrices. In the central limit theorem of linear spectral statistics for sample covariance matrices, the theoretical mean and covariance are computed numerically. Based on these numerical values, the power of the hypothesis test can be evaluated, and furthermore the confidence interval for the unknown parameters in the high-dimensional covariance matrix can be constructed. The validity of the proposed algorithms is well supported by a convergence theorem. Our numerical method is assessed by extensive simulation studies, and a real data example of the S&P 100 index data is analyzed to illustrate the proposed algorithms.

Suggested Citation

  • Lin, Ruitao & Liu, Zhongying & Zheng, Shurong & Yin, Guosheng, 2016. "Power computation for hypothesis testing with high-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 10-23.
    • Handle: RePEc:eee:csdana:v:104:y:2016:i:c:p:10-23
    DOI: 10.1016/j.csda.2016.05.008
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    References listed on IDEAS

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    1. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    2. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    3. Wang, Cheng, 2014. "Asymptotic power of likelihood ratio tests for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 184-189.
    4. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
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