Finding GM-estimators with global optimization techniques

Authors:
Rafael Blanquero;Emilio Carrizosa;Eduardo Conde
Affiliations:
Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Sevilla, Spain (e-mail: rblanque@cica.es;Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Sevilla, Spain (e-mail: ecarriz@cica.es;Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Sevilla, Spain (e-mail: educon@cica.es
Venue:
Journal of Global Optimization
Year:
2001

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Abstract

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.