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Finding GM-estimators with global optimization techniques
In this note we address the problem of finding the GM-estimator for the location parameter
of a univariate random variable. When this problem is non-convex but d.c. one can use a standard
covering method, which, in the one-dimensional 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 that this general-purpose algorithm
outperforms previous ad-hoc methods for this problem