The Annals of Statistics

Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices

Hendrik P. Lopuhaa and Peter J. Rousseeuw

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Abstract

Finite-sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices. The role of various equivariance properties is illustrated. The breakdown point is related to a measure of performance based on large deviations probabilities. Finally, we show that one-step reweighting preserves the breakdown point.

Article information

Source
Ann. Statist. Volume 19, Number 1 (1991), 229-248.

Dates
First available: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176347978

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176347978

Mathematical Reviews number (MathSciNet)
MR1091847

Zentralblatt MATH identifier
0733.62058

Subjects
Primary: 62F35: Robustness and adaptive procedures
Secondary: 62H12: Estimation

Keywords
Breakdown point affine equivariance tails of a distribution weighted mean and covariance

Citation

Lopuhaa, Hendrik P.; Rousseeuw, Peter J. Breakdown Points of Affine Equivariant Estimators of Multivariate Location and Covariance Matrices. The Annals of Statistics 19 (1991), no. 1, 229--248. doi:10.1214/aos/1176347978. http://projecteuclid.org/euclid.aos/1176347978.


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