A numerical method for minimum distance estimation problems

This paper introduces a general method for the numerical derivation of a minimum distance (MD) estimator for the parameters of an unknown distribution. The approach is based on an active sampling of the space in which the random sample takes values and on the optimization of the parameters of a suitable approximating model. This allows us to derive the MD estimator function for any given distribution, by which we can immediately obtain the MD estimate of the unknown parameters in correspondence to any observed random sample. Convergence of the method is proved when mild conditions on the sampling process and on the involved functions are satisfied, and it is shown that favorable rates can be obtained when suitable deterministic sequences are employed. Finally, simulation results are provided to show the effectiveness of the proposed algorithm on two case studies.