Random sets from the perspective of metric statistics
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918206017372160 |
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| author | Kurisu, Daisuke Okamoto, Yuta Otsu, Taisuke |
| author_facet | Kurisu, Daisuke Okamoto, Yuta Otsu, Taisuke |
| contents | 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 Fréchet means, and presents some applications of metric statistics to econometric problems involving random sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13440 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random sets from the perspective of metric statistics Kurisu, Daisuke Okamoto, Yuta Otsu, Taisuke Statistics Theory Econometrics 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 Fréchet means, and presents some applications of metric statistics to econometric problems involving random sets. |
| title | Random sets from the perspective of metric statistics |
| topic | Statistics Theory Econometrics |
| url | https://arxiv.org/abs/2511.13440 |