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New algorithms for M-estimation of multivariate scatter and location

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  • Dümbgen, Lutz
  • Nordhausen, Klaus
  • Schuhmacher, Heike

Abstract

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and other algorithms. The main idea is to utilize a Taylor expansion of second order of the target functional and devise a partial Newton–Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:200-217
    DOI: 10.1016/j.jmva.2015.11.009
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    References listed on IDEAS

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    1. Sirkiä, Seija & Taskinen, Sara & Oja, Hannu, 2007. "Symmetrised M-estimators of multivariate scatter," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1611-1629, September.
    2. Nordhausen, Klaus & Oja, Hannu & Tyler, David E., 2008. "Tools for Exploring Multivariate Data: The Package ICS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i06).
    3. David E. Tyler & Frank Critchley & Lutz Dümbgen & Hannu Oja, 2009. "Invariant co‐ordinate selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 549-592, June.
    4. Klaus Nordhausen & David E. Tyler, 2015. "A cautionary note on robust covariance plug-in methods," Biometrika, Biometrika Trust, vol. 102(3), pages 573-588.
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    Cited by:

    1. Hosseini, Reshad & Sra, Suvrit & Theis, Lucas & Bethge, Matthias, 2016. "Inference and mixture modeling with the Elliptical Gamma Distribution," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 29-43.
    2. 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.
    3. Romanov, Elad & Kur, Gil & Nadler, Boaz, 2023. "Tyler’s and Maronna’s M-estimators: Non-asymptotic concentration results," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    4. Frahm, Gabriel & Nordhausen, Klaus & Oja, Hannu, 2020. "M-estimation with incomplete and dependent multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    5. Pokojovy, Michael & Jobe, J. Marcus, 2022. "A robust deterministic affine-equivariant algorithm for multivariate location and scatter," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).

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