ELSEVIER Computational Statistics & Data Analysis 25 (1997) 1-15 COMPUTATIONAL STATISTICS & DATA ANALYSIS On the computation and efficiency of a HBP-GM estimator some simulation results Jeroen Hinloopen*, Rien Wagenvoort Department of Economics, European University Institute, 1-50016 San Domenico di Fiesole (F1), Italy Received July 1996; revised September 1996 Abstract We propose and test a specific correction factor which improves both the resamplino 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. © 1997 Elsevier Science B.V. Keywords: LMS; MVE; Resampling algorithm; Projection algorithm; Efficiency JEL Classification: C13, C15 1. Introduction It is widely held that generalised M (GM) or bounded-influence estimators for the unknown parameters of the linear model have two undesirable properties. First, their breakdown point (which is the minimum fraction of data contamination that causes an estimator to take on any value, see Donoho and Huber, 1983), is at most 1/(p + 1), where p is the number of explanatory variables (see Maronna et al., 1979). For any p of reasonable size this is well below 50%, the breakdown point which * Corresponding author. 0167-9473/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PII S0 1 67-9473(96)0008 3-7