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RDS free CLT for spiked eigenvalues of high-dimensional covariance matrices

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  • Liu, Yan
  • Bai, Zhidong
  • Li, Hua
  • Hu, Jiang
  • Lv, Zhihui
  • Zheng, Shurong

Abstract

In this paper, we extend the CLT for sample spiked eigenvalues in the generalized spiked covariance model proposed in Jiang and Bai (2021a) to the case where RDS is considered free, i.e., except for an upper limit of the RDS to guarantee that the spiked eigenvalue is distant, there is no limit for p/n, which is the Ratio of Dimension to sample Size (RDS). Therefore, the choice of dimensionality and sample size is more flexible in our regime.

Suggested Citation

  • Liu, Yan & Bai, Zhidong & Li, Hua & Hu, Jiang & Lv, Zhihui & Zheng, Shurong, 2022. "RDS free CLT for spiked eigenvalues of high-dimensional covariance matrices," Statistics & Probability Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s0167715222000827
    DOI: 10.1016/j.spl.2022.109501
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Bai, Zhidong & Yao, Jianfeng, 2012. "On sample eigenvalues in a generalized spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 167-177.
    3. Seunggeun Lee & Fei Zou & Fred A. Wright, 2014. "Convergence of sample eigenvalues, eigenvectors, and principal component scores for ultra-high dimensional data," Biometrika, Biometrika Trust, vol. 101(2), pages 484-490.
    4. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    5. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    6. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
    7. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
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