Abstract
Robust estimation of location and scale in the presence of outliers is an important task in classification. Outlier sensitive estimation will lead to a large number of misclassifications. Rousseeuw introduced two estimators with high breakdown point, namely the minimum-volume-ellipsoid estimator (MVE) and the minimum-covariance-determinant estimator (MCD). While the MCD estimator has better theoretical properties than the MVE, the latter one appears to be used more widely. This may be due to the lack of fast algorithms for computing the MCD, up to now.
In this paper two branch-and-bound algorithms for the exact computation of the MCD are presented. The results of their application to simulated samples are compared with a new heuristic algorithm “multistart iterative trimming” and the steepest descent method suggested by Hawkins. The results show that multistart iterative trimming is a good and very fast heuristic for the MCD which can be applied to samples of large size.
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References
BUTLER, R. W. and DAVIES, P. L. and Jhun, M. (1993): Asymptotics for the Minimum Covariance Determinant Estimator. The Annals of Statistics, 21, No. 3, 1385–1400.
DAVIES, L. (1992): The Asymptotics of Rousseeuw’s Minimum Volume Ellipsoid Estimator. The Annals of Statistics, 20, No. 4, 1828–1843.
GNANADESIKAN, R. and KETTENRING, J. R. (1972): Robust Estimates, Re- siduals, and Outlier Detection with Multiresponse Data. Biometrics, 28, 81–124
HAWKINS, D. M. (1994): The feasible solution algorithm for the minimum covariance determinant estimator in multivariate data. Computational Statistics e4 Data Analysis, 17, 197–210.
PESCH, C. (1998): Fast Computation of the Minimum Covariance Determinant Estimator. MIP-9806, Technical Report, Fakultät für Mathematik und Informatik, Universität Passau, 94030 Passau, Germany.
PREPARATA, F. P. and SHAMOS, M. I. (1988): Computational geometry. Springer Verlag, New York.
ROUSSEEUW, P. J. (1983): Multivariate Estimation with High Breakdown Point. In Mathematical statistics and applications: Proc. 4th Pannonian Symp. Math. Stat., Bad Tatzmannsdorf, Austria. 283–297.
ROUSSEEUW, P. J. and VAN DRIESSEN, K. (1997): A Fast Algorithm for the Minimum Covariance Determinant Estimator. Preprint. Technical Report, University of Antwerp, Submitted for publication. http://win-www.uia.ac.be/u/statis/publicat/fastmcdseadme.html
ROUSSEEUW, P. J. and LEROY, A. M. (1987): Robust Regression and Outlier Detection. John Wiley & Sons, Inc.
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© 1999 Springer-Verlag Berlin · Heidelberg
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Pesch, C. (1999). Computation of the Minimum Covariance Determinant Estimator. In: Gaul, W., Locarek-Junge, H. (eds) Classification in the Information Age. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60187-3_22
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DOI: https://doi.org/10.1007/978-3-642-60187-3_22
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