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Minimum volume ellipsoid

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Abstract The minimum volume ellipsoid (MVE) estimator is based on the smallest volume ellipsoid that covers h of the n observations. It is an affine equivariant, high‐breakdown robust estimator of multivariate location and scatter. The MVE can be computed by a resampling algorithm. Its low bias makes the MVE very useful for outlier detection in multivariate data, often through the use of MVE‐based robust distances. We review the basic MVE definition as well as some useful extensions such as the one‐step reweighted MVE. We discuss the main properties of the MVE including its breakdown value, affine equivariance, and efficiency. We discuss the basic resampling algorithm to calculate the MVE and illustrate its use on two examples. An overview of applications is given, as well as some related classes of robust estimators of multivariate location and scatter. Copyright © 2009 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods

Distances of the observations in the pulp fiber dataset based on the four pulp fiber properties: (a) Mahalanobis distances based on sample mean and sample covariance matrix; (b) Robust distances based on MVE estimates of location and scatter. The horizontal cutoff line in both panels is at .

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MVE‐based robust distances of the observations in the Philips dataset. The horizontal cutoff line is at .

[ Normal View | Magnified View ]

Pairwise scatterplots of the four pulp fiber variables. The ellipses represent the 97.5% tolerance ellipsoid for the observations, based on the MVE estimates of location and scatter .

[ Normal View | Magnified View ]

Pairwise scatterplots of the four pulp fiber variables. The ellipses represent the 97.5% tolerance ellipsoid for the observations, based on the sample mean and sample covariance matrix.

[ Normal View | Magnified View ]

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Statistical and Graphical Methods of Data Analysis > Robust Methods

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