Random sets from the perspective of metric statistics

TL;DR

This paper explores the connection between random set theory and metric statistics, clarifying the relationship between Aumann and Fréchet means, and applying these concepts to econometric models involving random sets.

Contribution

It establishes a theoretical link between Aumann and Fréchet means and demonstrates their application in econometric analysis of random sets.

Findings

Clarifies the relationship between Aumann and Fréchet means.

Provides applications of metric statistics to econometric problems.

Enhances understanding of random sets in metric spaces.

Abstract

Since the seminal work by Beresteanu and Molinari(2008), the random set theory and related inference methods have been widely applied in partially identified econometric models. Meanwhile, there is an emerging field in statistics for studying random objects in metric spaces, called metric statistics. This paper clarifies a relationship between two fundamental concepts in these literatures, the Aumann and Fr\'echet means, and presents some applications of metric statistics to econometric problems involving random sets.