Bootstrap confidence sets for the Aumann mean of a random closed set

The objective is to develop a reliable method to build confidence sets for the Aumann mean of a random closed set as estimated through the Minkowski empirical mean. First, a general definition of the confidence set for the mean of a random set is provided. Then, a method using a characterization of the confidence set through the support function is proposed and a bootstrap algorithm is described, whose performance is investigated in Monte Carlo simulations.