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Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator

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  • Croux, Christophe
  • Haesbroeck, Gentiane

Abstract

The minimum covariance determinant (MCD) scatter estimator is a highly robust estimator for the dispersion matrix of a multivariate, elliptically symmetric distribution. It is relatively fast to compute and intuitively appealing. In this note we derive its influence function and compute the asymptotic variances of its elements. A comparison with the one step reweighted MCD and with S-estimators is made. Also finite-sample results are reported.

Suggested Citation

  • Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
  • Handle: RePEc:eee:jmvana:v:71:y:1999:i:2:p:161-190
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    References listed on IDEAS

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    1. Hawkins, Douglas M., 1994. "The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 197-210, February.
    2. Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
    3. Davies, Laurie, 1992. "An efficient Fr├ęchet differentiable high breakdown multivariate location and dispersion estimator," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 311-327, February.
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