On the Computation and Efficiency of A Hbp-Gm Estimator Some Simulation Results

Abstract

We propose and test a specific correction factor which improves both the resampling and projection algorithm for approximating the minimum volume ellipsoid (MVE) estimator. Simulations show that a high-breakdown-point GM estimator, based among other things on these improved MVE-estimates of location and scatter (i) is little less efficient than OLS if data are free from outlying observations, but in most cases is much more efficient if outliers corrupt the data, (ii) is always more efficient than Rousseeuw's least median of squares (LMS) estimator, and (iii) is always superior to both LMS and OLS if both precision and efficiency are considered. (C) 1997 Elsevier Science B.V.