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 a new procedure based on the support function.
Confidence Sets for the Aumann Mean of a Random Closed Set
SERI, RAFFAELLO
2000-01-01
Abstract
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 a new procedure based on the support function.
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