Parametric Multivariate Density Estimation Using L2 Distance: a Simulation Study on Robustness

Purpose of this work is to investigate on the use of $L_2$ distance as a practical tool for parameters estimation of multivariate probability densities in all those situations involving the study of large data sets where outliers may be present, situations in which maximum likelihood estimators are usually unstable. Theory is outlined and some examples are proposed. In order to evaluate robustness of Maximum Likelihood and L_2 estimators, we compare the results arising from Montecarlo simulation for some bivariate densities in occurrence of different outliers positioning and consistency. Specific routines were implemented in R computing environment.