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Minimum covariance determinant and extensions

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The minimum covariance determinant (MCD) method is a highly robust estimator of multivariate location and scatter, for which a fast algorithm is available. Since estimating the covariance matrix is the cornerstone of many multivariate statistical methods, the MCD is an important building block when developing robust multivariate techniques. It also serves as a convenient and efficient tool for outlier detection. The MCD estimator is reviewed, 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 applied and methodological multivariate statistics. Two recent extensions of the MCD are described. The first one is a fast deterministic algorithm which inherits the robustness of the MCD while being almost affine equivariant. The second is tailored to high‐dimensional data, possibly with more dimensions than cases, and incorporates regularization to prevent singular matrices. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Robust Methods Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery
Bivariate wine data: tolerance ellipse of the classical mean and covariance matrix (red), and that of the robust location and scatter matrix (blue)
[ Normal View | Magnified View ]
Distance‐distance plot of the full 13‐dimensional wine data set
[ Normal View | Magnified View ]
(a) Mahalanobis distances and (b) robust distances for the bivariate wine data
[ Normal View | Magnified View ]

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Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery
Statistical and Graphical Methods of Data Analysis > Robust Methods
Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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