On Robustness to Outliers of Parametric L2 Estimate Criterion in the case of Bivariate Normal Mixtures: a Simulation Study

Purpose of this work is to investigate on the use of the Integrated Squared Error, or L_2-distance, as a practical tool for parameters estimation of mixtures of two normal bivariates in presence of outliers, situations in which maximum likelihood estimators (MLE) are usually unstable. Following Scott (2001), theory is outlined, closed expressions for the L_2 minimizing estimate criterion (L_2E) for bivariate normal mixtures are presented (Wand and Jones, 1995) and some examples are proposed. In order to evaluate robustness of MLE and L_2E, the latter being by nature less influenced by outliers (Basu et alia, 1998), we compare results arising from Montecarlo simulation for some mixtures of normal bivariates in occurrence of different outliers positioning and consistency.