Abstract
Abstract : The existence of outliers in a data set and how to deal with them is an important problem in statistics. The Minimum Volume Ellipsoid (MVE) estimator is a robust estimator of location and shape; however its use has been limited because few computationally attractive methods exist to calculate it. Determining the MVE consists of two parts: finding the subset of points to be used in the estimate and finding the ellipse that covers this set. This paper will address the first problem. The proposed method of subset selection is called the Effective Independence Distribution (ElD) method which chooses the subset by mnimizing determinants of matrices containing the data. This method is deterministic yielding reproducible estimates of location and scatter for a given data set. The ElD method of finding the MVE is applied to several regression data sets where the true estimate is known. Results show that the EID method produces the subset of data in less than a second and that there is less than 6% relative error in the estimates. (AN)
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