Advanced Review
Minimum covariance determinant
Mia Hubert,
Michiel Debruyne,
Corresponding Author
Mia Hubert
Department of Mathematics-LStat, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Department of Mathematics-LStat, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, BelgiumSearch for more papers by this authorMichiel Debruyne
Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium
Search for more papers by this authorMia Hubert,
Michiel Debruyne,
Corresponding Author
Mia Hubert
Department of Mathematics-LStat, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Department of Mathematics-LStat, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, BelgiumSearch for more papers by this authorMichiel Debruyne
Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium
Search for more papers by this authorThis article has been updated at: Minimum covariance determinant and extensions.
Abstract
The minimum covariance determinant (MCD) estimator is a highly robust estimator of multivariate location and scatter. It can be computed efficiently with the FAST-MCD algorithm of Rousseeuw and Van Driessen. Since estimating the covariance matrix is the cornerstone of many multivariate statistical methods, the MCD has also been used to develop robust and computationally efficient multivariate techniques.
In this paper, we review the MCD estimator, along with its main properties such as affine equivariance, breakdown value, and influence function. We discuss its computation, and list applications and extensions of the MCD in theoretical and applied multivariate statistics. Copyright © 2009 John Wiley & Sons, Inc.
This article is categorized under:
- Statistical and Graphical Methods of Data Analysis > Robust Methods
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