Finding GM-estimators with global optimization techniques

In this note we address the problem of finding the GM-estimator for the loc ation parameter of a univariate random variable. When this problem is non-c onvex but d.c. one can use a standard covering method, which, in the one-di mensional case has a simple form. In this paper we exploit the structure of the problem in order to obtain d.c. decompositions with certain optimality properties in the application of the algorithm. Numerical results show tha t this general-purpose algorithm outperforms previous ad-hoc methods for th is problem.