Deepest Points and Least Deep Points: Robustness and Outliers with MZE
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Multivariate outlier identification is often based on robust location and scatter estimates and usually performed relative to an elliptically shaped distribution. On the other hand, the idea of outlying observations is closely related to the notion of data depth, where observations with minimum depth are potential outliers. Here, we are not generally bound to the idea of an elliptical shape of the underlying distribution. Koshevoy and Mosler (1997) introduced zonoid trimmed regions which define a data depth. Recently, Paris Scholz (2002) and Becker and Paris Scholz (2004) investigated a new approach for robust estimation of convex bodies resulting from zonoids. We follow their approach and explore how the minimum volume zonoid (MZE) estimators can be used for multivariate outlier identification in the case of non-elliptically shaped null distributions.
KeywordsConvex Body Data Depth Robust Estimator Deep Point Breakdown Point
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