Most multivariate statistical analyses rely on estimation of the location and dispersion of a high-dimensional data set. The classical estimators for dealing with this are the empirical average and covariance matrix. However, these estimators are vulnerable to even small amounts of contamination in the sample. Robust alternatives are therefore needed. In this talk, focus is on the Minimum Covariance Determinant (MCD) estimator defined by Rousseeuw in 1985. This estimator will be used to introduce some of the main tools available in robust statistics to measure the robustness of a given procedure, i.e. the influence function and the maxbias curve. Also the computational complexity of the MCD technique will be discussed.

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