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The multivariate least-trimmed squares estimator

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  • Agulló, Jose
  • Croux, Christophe
  • Van Aelst, Stefan

Abstract

In this paper we introduce the least-trimmed squares estimator for multivariate regression. We give three equivalent formulations of the estimator and obtain its breakdown point. A fast algorithm for its computation is proposed. We prove Fisher-consistency at the multivariate regression model with elliptically symmetric error distribution and derive the influence function. Simulations investigate the finite-sample efficiency and robustness of the estimator. To increase the efficiency of the estimator, we also consider a one-step reweighted estimator.

Suggested Citation

  • Agulló, Jose & Croux, Christophe & Van Aelst, Stefan, 2008. "The multivariate least-trimmed squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 311-338, March.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:311-338
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    1. Esa Ollila & Hannu Oja & Thomas P. Hettmansperger, 2002. "Estimates of regression coefficients based on the sign covariance matrix," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 447-466, August.
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    5. 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.
    6. Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
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    Cited by:

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    8. Cabana Garceran del Vall, Elisa & Lillo Rodríguez, Rosa Elvira & Laniado Rodas, Henry, 2019. "Shrinkage reweighted regression," DES - Working Papers. Statistics and Econometrics. WS 28500, Universidad Carlos III de Madrid. Departamento de Estadística.
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