A DETERMINISTIC METHOD FOR ROBUST ESTIMATION OF MULTIVARIATE LOCATIONAND SHAPE

The existence of outliers in a data set and how to deal with them is a n important problem in statistics. The minimum volume ellipsoid (MVE) estimator is a robust estimator of location and covariate structure: h owever its use has been limited because there an few computationally a ttractive methods. Determining the MVE consists of two parts-finding t he subset of points to be used in the estimate and finding the ellipso id that covers this set. This article addresses the first problem. Our method H-ill also allow us to compute the minimum covariance determin ant (MCD, estimator, The proposed method of subset selection is called the effective independence distribution (EID) method. which chooses t he subset by minimizing determinants of matrices containing the data. This method is deterministic. yielding reproducible estimates of locat ion and scatter for a given data set. The EID method of finding the MV E is applied to several regression data sets where tile true estimate is known. Results show that the EID method. when applied to these data sets. produces the subset of data more quickly than conventional proc edures and that there is less than 6% relative error in the estimates. We also give timing results illustrating the feasibility of our metho d fbr larger data arts. For the case of 10,000 points in 10 dimensions , the compute time is under 25 minutes.