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A cautionary note on robust covariance plug-in methods

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  • Klaus Nordhausen
  • David E. Tyler

Abstract

The sample covariance matrix, which is well known to be highly nonrobust, plays a central role in many classical multivariate statistical methods. A popular way of making such multivariate methods more robust is to replace the sample covariance matrix with some robust scatter matrix. The aim of this paper is to point out that multivariate methods often require that certain properties of the covariance matrix hold also for the robust scatter matrix in order for the corresponding robust plug-in method to be a valid approach, but that not all scatter matrices possess the desired properties. Plug-in methods for independent components analysis, observational regression and graphical modelling are considered in more detail. For each case, it is shown that replacing the sample covariance matrix with a symmetrized robust scatter matrix yields a valid robust multivariate procedure.

Suggested Citation

  • Klaus Nordhausen & David E. Tyler, 2015. "A cautionary note on robust covariance plug-in methods," Biometrika, Biometrika Trust, vol. 102(3), pages 573-588.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:3:p:573-588.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv022
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    References listed on IDEAS

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    1. Christophe Croux & Stefan Aelst & Catherine Dehon, 2003. "Bounded influence regression using high breakdown scatter matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 265-285, June.
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    Cited by:

    1. Loperfido, Nicola, 2021. "Some theoretical properties of two kurtosis matrices, with application to invariant coordinate selection," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Jari Miettinen & Markus Matilainen & Klaus Nordhausen & Sara Taskinen, 2020. "Extracting Conditionally Heteroskedastic Components using Independent Component Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 293-311, March.
    3. Dümbgen, Lutz & Nordhausen, Klaus & Schuhmacher, Heike, 2016. "New algorithms for M-estimation of multivariate scatter and location," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 200-217.
    4. Virta, J., 2016. "One-step M-estimates of scatter and the independence property," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 133-136.
    5. Nordhausen, Klaus & Ruiz-Gazen, Anne, 2022. "On the usage of joint diagonalization in multivariate statistics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Xin Dang & Hailin Sang & Lauren Weatherall, 2019. "Gini covariance matrix and its affine equivariant version," Statistical Papers, Springer, vol. 60(3), pages 641-666, June.
    7. Archimbaud, Aurore & Nordhausen, Klaus & Ruiz-Gazen, Anne, 2018. "ICS for multivariate outlier detection with application to quality control," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 184-199.
    8. Klaus Nordhausen & Anne Ruiz-Gazen, 2022. "On the usage of joint diagonalization in multivariate statistics," Post-Print hal-04296111, HAL.
    9. Archimbaud, Aurore & Boulfani, Fériel & Gendre, Xavier & Nordhausen, Klaus & Ruiz-Gazen, Anne & Virta, Joni, 2021. "ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control," TSE Working Papers 21-1182, Toulouse School of Economics (TSE), revised Mar 2022.
    10. Miettinen, Jari & Nordhausen, Klaus & Taskinen, Sara, 2017. "Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i02).
    11. Nordhausen, Klaus & Oja, Hannu & Tyler, David E., 2022. "Asymptotic and bootstrap tests for subspace dimension," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Ruiz-Gazen, Anne & Thomas-Agnan, Christine & Laurent, Thibault & Mondon, Camille, 2022. "Detecting outliers in compositional data using Invariant Coordinate Selection," TSE Working Papers 22-1320, Toulouse School of Economics (TSE).

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