Asymptotic properties and robustness of minimum dissimilarity estimators of location-scale parameters

This paper deals with the asymptotic properties of an unexplored estimation method, for location and scale parameters, based on the minimization of the Monge–Gini–Kantorovich–Wasserstein distance. This method is rigorously defined and justified according to the general principle which directs the theory of regression. The resulting estimators — called minimum dissimilarity estimators — exist, and are measurable, consistent, and robust. Their asymptotic distribution is the same as the probability distribution of the absolute minimum point of an interesting functional of a standard Brownian bridge. This fact can be employed to obtain both explicit exact expressions and numerical approximations for the above asymptotic distribution.