Confidence sets for the Aumann mean of a random closed set

The objective of this paper is to develop a set of reliable methods to build confidence sets for the Aumann mean of a random closed set estimated through the Minkowski empirical mean. In order to do so, we introduce a procedure to build a confidence set based on Weil’s result for the Hausdorff distance between the empirical and the Aumann means; then, we introduce another procedure based on the support function.