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Convergence of sample eigenvalues, eigenvectors, and principal component scores for ultra-high dimensional data

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  • Seunggeun Lee
  • Fei Zou
  • Fred A. Wright

Abstract

The development of high-throughput biomedical technologies has led to increased interest in the analysis of high-dimensional data where the number of features is much larger than the sample size. In this paper, we investigate principal component analysis under the ultra-high dimensional regime, where both the number of features and the sample size increase as the ratio of the two quantities also increases. We bridge the existing results from the finite and the high-dimension low sample size regimes, embedding the two regimes in a more general framework. We also numerically demonstrate the universal application of the results from the finite regime.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:2:p:484-490.
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    File URL: http://hdl.handle.net/10.1093/biomet/ast064
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    Cited by:

    1. 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).
    2. Chung, Hee Cheol & Ahn, Jeongyoun, 2021. "Subspace rotations for high-dimensional outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    3. Mei Choi Chiu & Chi Seng Pun & Hoi Ying Wong, 2017. "Big Data Challenges of High‐Dimensional Continuous‐Time Mean‐Variance Portfolio Selection and a Remedy," Risk Analysis, John Wiley & Sons, vol. 37(8), pages 1532-1549, August.
    4. Dey, Rounak & Lee, Seunggeun, 2019. "Asymptotic properties of principal component analysis and shrinkage-bias adjustment under the generalized spiked population model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 145-164.
    5. Pun, Chi Seng & Wong, Hoi Ying, 2019. "A linear programming model for selection of sparse high-dimensional multiperiod portfolios," European Journal of Operational Research, Elsevier, vol. 273(2), pages 754-771.

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