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Random sets from the perspective of metric statistics

Author

Listed:
  • Daisuke Kurisu
  • Yuta Okamoto
  • Taisuke Otsu

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.

Suggested Citation

  • Daisuke Kurisu & Yuta Okamoto & Taisuke Otsu, 2025. "Random sets from the perspective of metric statistics," Papers 2511.13440, arXiv.org.
    • Handle: RePEc:arx:papers:2511.13440
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    References listed on IDEAS

    as
    1. Kurisu, Daisuke & Otsu, Taisuke, 2025. "Model averaging for global Fréchet regression," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    2. Molchanov,Ilya & Molinari,Francesca, 2018. "Random Sets in Econometrics," Cambridge Books, Cambridge University Press, number 9781107121201, January.
    3. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    4. Kurisu, Daisuke & Otsu, Taisuke, 2025. "Model averaging for global Fréchet regression," LSE Research Online Documents on Economics 126533, London School of Economics and Political Science, LSE Library.
    5. Danielle C. Tucker & Yichao Wu & Hans-Georg Müller, 2023. "Variable Selection for Global Fréchet Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1023-1037, April.
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