Daisuke Kurisu, Yuta Okamoto, Taisuke Otsu
arXiv 17 Nov 2025 · Mathematics — Statistics Theory
arXiv:2511.13440 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by appendix_command · 50% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Beresteanu, Arie and Molinari, Francesca (2008) Asymptotic properties for a class of partially identified models | 1.000 | 6 | 4 | 100% |
| 2 | Petersen, Alexander and Müller, Hans-Georg (2019) Fréchet regression for random objects with Euclidean predictors | 0.843 | 5 | 3 | 60% |
| 3 | Kurisu, Daisuke and Zhou, Yidong and Otsu, Taisuke and Müller, Hans-… (2024) Geodesic causal inference self | 0.737 | 5 | 2 | 60% |
| 4 | Dubey, Paromita and Chen, Yaqing and Müller, Hans-Georg (2024) Metric statistics: Exploration and inference for random objects with distance profiles | 0.737 | 3 | 2 | 100% |
| 5 | Molchanov, Ilya (2017) Theory of Random Sets | 0.737 | 3 | 2 | 100% |
| 6 | Kurisu, Daisuke and Zhou, Yidong and Otsu, Taisuke and Müller, Hans-… (2025) Regression Discontinuity Designs for Functional Data and Random Objects in Geodesic Spaces self | 0.644 | 2 | 2 | 100% |
| 7 | Molinari, Francesca (2020) Microeconometrics with partial identification | 0.644 | 2 | 2 | 100% |
| 8 | Molchanov, Ilya and Molinari, Francesca (2018) Random Sets in Econometrics | 0.644 | 2 | 2 | 100% |
| 9 | Aumann, R J (1965) Integrals of set valued functions | 0.405 | 1 | 1 | 100% |
| 10 | Bhattacharjee, Satarupa and Li, Bing and Wu, Xiao and Xue, Lingzhou (2025) Doubly robust estimation of causal effects for random object outcomes with continuous treatments | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Lee bounds for random objects | 0.737 | 3 | 2 |