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Robust Estimation

of Multivariate Location and Covariance

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Standard statistics, such as the sample mean and covariance, are
sometimes applied without serious thought to their appropriateness.
In the case of the sample mean and covariance, this is largely due to
their squared-error optimality under i.i.d. conditions; however, these
estimates are not robust to deviations from the model. In fact, the
estimates can be made arbitrarily poor, by the corruption of a single
data point. It is the goal of robust estimation to develop methods
that are not only robust to outliers, but also perform well under the
correct model.

In this paper, we review robust estimation techniques specifically
tailored to estimating multivariate location and scatter. Particular
attention will be paid to three methods: M-estimators, S-estimators,
and the Minimum Covariance Determinant (MCD) estimator. The intuition
behind these estimators is to find the location and covariance
estimate by trying to simultaneously identify and down-weight outliers
in your estimates; although, they do so in different ways.

Last updated: Jan. 26, 2000.

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