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Lee Bounds for Random Objects

Daisuke Kurisu, Yuta Okamoto, Taisuke Otsu

arXiv 14 Jan 2026 · Econometrics

arXiv:2601.09453 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as compositional and distributional data. By exploiting a representation of the Fréchet mean of the potential outcome via embedding in an Euclidean or Hilbert space, we present a feasible characterization of the identified set of the causal effect of interest, and then propose its analog estimator and bootstrap confidence region. The proposed method is illustrated by numerical examples on compositional and distributional data.

Citation extraction

58
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in-text mentions
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distinct cited
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Lee, D. S (2009) Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects1.00073100%
2Beresteanu, A. and Molinari, F (2008) Asymptotic properties for a class of partially identified models0.73732100%
3Kurisu, D., Okamoto, Y., and Otsu, T (2025) Random sets from the perspective of metric statistics self0.73732100%
4Kurisu, D., Zhou, Y., Otsu, T., and Müller, H.-G (2024) Geodesic causal inference self0.73732100%
5Dubey, P., Chen, Y., and Mülller, H.-G (2024) Metric statistics: exploration and inference for random objects with distance profiles0.64422100%
6Gunsilius, F. F (2023) Distributional Synthetic Controls0.64422100%
7Bessone, P., Rao, G., Schilbach, F., Schofield, H., and Toma, M (2021) The Economic Consequences of Increasing Sleep Among the Urban Poor0.58531100%
8Horowitz, J. L. and Manski, C. F (1995) Identification and Robustness with Contaminated and Corrupted Data0.58531100%
9Zhou, Y. and Müller, H.-G (2022) Network regression with graph Laplacians0.51121100%
10Aitchison, J (1982) The Statistical Analysis of Compositional Data0.40511100%

Showing the top 10 of 58 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Conformalized Lee Inference: Distribution-Free Individual Treatment Effect Intervals under Monotone Sample Selection0.51121
2IV regression with distribution-valued outcomes0.40511