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This is the web page for my area exam. It is intended for members of my committee but is available to the general public in case anyone finds it useful. It will serve primarily as a repository for relevant papers and scheduling information.
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.