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Robust and efficient estimation of multivariate scatter and location Maronna, Ricardo


We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It is important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that is, a low bias under contamination. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-Estimators with a monotonic weight function like the bisquare have a low efficiency for small p, and their efficiency tends to one with increasing p. Unfortunately, this advantage is paid for by a serious loss of robustness for large p. We consider four families of estimators with controllable efficiencies whose performance for moderate to large p has not been explored to date: S-estimators with a non-monotonic weight function (Rocke 1996), MM-estimators, -estimators, and the Stahel-Donoho estimator. Two types of starting estimators are employed: the MVE computed through subsampling, and a semi-deterministic procedure proposed by Pea and Prieto (2007) for outlier detection. A simulation study shows that the Rocke estimator starting from the Pea-Prieto estimator and with an adequate tuning, can simultaneously attain high efficiency and high robustness for p, and the MM estimator can be recommended for p¡15.

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