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Scale-Invariant Sparse PCA on High-Dimensional Meta-Elliptical Data

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  • Fang Han
  • Han Liu

Abstract

We propose a semiparametric method for conducting scale-invariant sparse principal component analysis (PCA) on high-dimensional non-Gaussian data. Compared with sparse PCA, our method has a weaker modeling assumption and is more robust to possible data contamination. Theoretically, the proposed method achieves a parametric rate of convergence in estimating the parameter of interests under a flexible semiparametric distribution family; computationally, the proposed method exploits a rank-based procedure and is as efficient as sparse PCA; empirically, our method outperforms most competing methods on both synthetic and real-world datasets.

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  • Fang Han & Han Liu, 2014. "Scale-Invariant Sparse PCA on High-Dimensional Meta-Elliptical Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 275-287, March.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:275-287
    DOI: 10.1080/01621459.2013.844699
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    Cited by:

    1. He, Yong & Zhang, Liang & Ji, Jiadong & Zhang, Xinsheng, 2019. "Robust feature screening for elliptical copula regression model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 568-582.
    2. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    3. Davy Paindaveine & Julien Remy & Thomas Verdebout, 2017. "Testing for Principal Component Directions under Weak Identifiability," Working Papers ECARES ECARES 2017-37, ULB -- Universite Libre de Bruxelles.
    4. Niu, Lu & Liu, Xiumin & Zhao, Junlong, 2020. "Robust estimator of the correlation matrix with sparse Kronecker structure for a high-dimensional matrix-variate," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    5. Langworthy, Benjamin W. & Stephens, Rebecca L. & Gilmore, John H. & Fine, Jason P., 2021. "Canonical correlation analysis for elliptical copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    6. Deng, Kaihua, 2016. "A test of asymmetric comovement for state-dependent stock returns," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 68-85.
    7. Kim, Seungkyu & Park, Seongoh & Lim, Johan & Lee, Sang Han, 2023. "Robust tests for scatter separability beyond Gaussianity," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    8. Fan, Jianqing & Wang, Weichen & Zhong, Yiqiao, 2019. "Robust covariance estimation for approximate factor models," Journal of Econometrics, Elsevier, vol. 208(1), pages 5-22.
    9. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).

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