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On the number of principal components in high dimensions

Author

Listed:
  • Sungkyu Jung
  • Myung Hee Lee
  • Jeongyoun Ahn

Abstract

SUMMARYWe consider how many components to retain in principal component analysis when the dimension is much higher than the number of observations. To estimate the number of components, we propose to sequentially test skewness of the squared lengths of residual scores that are obtained by removing leading principal components. The residual lengths are asymptotically left-skewed if all principal components with diverging variances are removed, and right-skewed otherwise. The proposed estimator is shown to be consistent, performs well in high-dimensional simulation studies, and provides reasonable estimates in examples.

Suggested Citation

  • Sungkyu Jung & Myung Hee Lee & Jeongyoun Ahn, 2018. "On the number of principal components in high dimensions," Biometrika, Biometrika Trust, vol. 105(2), pages 389-402.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:2:p:389-402.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy010
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    Citations

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    Cited by:

    1. Chung, Hee Cheol & Ahn, Jeongyoun, 2021. "Subspace rotations for high-dimensional outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Kazuyoshi Yata & Makoto Aoshima, 2020. "Geometric consistency of principal component scores for high‐dimensional mixture models and its application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 899-921, September.
    3. Yuefeng Han & Rong Chen & Cun-Hui Zhang, 2020. "Rank Determination in Tensor Factor Model," Papers 2011.07131, arXiv.org, revised May 2022.

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