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Identification and Inference for Algorithmic Frontiers with Selective Labels

Yiqi Liu, Francesca Molinari, Amilcar Velez

arXiv 12 Jun 2026 · Econometrics

arXiv:2606.14977 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper provides identification results to characterize a fairness-accuracy (FA) frontier, and statistical inference tools to test hypotheses and build a confidence set for the FA-frontier, when outcomes are observed only for selected individuals. When the selection process is unrestricted but loss is measured in specific ways, we provide a characterization of the sharp identification region of the FA-frontier. Under an assumption of unconfoundedness conditional on observables (and unrestricted loss functions), we obtain point identification and propose a debiased machine learning estimator, derive its asymptotic distribution, and show how this can be used to carry out inference for the FA-frontier. In work in progress, we extend the partial identification results to a broader class of loss functions.

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57
references
127
in-text mentions
57
distinct cited
7
self-citations
31,773
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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
1Liu, Yiqi and Francesca Molinari (2026) Inference for an Algorithmic Fairness-Accuracy Frontier self1.000236100%
2Liang, Annie, Jay Lu, Xiaosheng Mu, and Kyohei Okumura (2026) Algorithm Design: A Fairness-Accuracy Frontier1.000153100%
3Chernozhukov, Victor, Denis Chetverikov, Mert Demirer, Esther Duflo,… (2018) Double/debiased machine learning for treatment and structural parameters1.00063100%
4Schneider, Rolf (1993) Convex Bodies: The Brunn-Minkowski Theory0.92843100%
5Fang, Zheng and Andres Santos (2019) Inference on directionally differentiable functions0.87482100%
6Bontemps, Christian, Thierry Magnac, and Eric Maurin (2012) Set identified linear models0.73732100%
7Rambachan, Ashesh, Amanda Coston, and Edward H. Kennedy (2025) Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding0.73732100%
8Molchanov, I (2017) Theory of Random Sets0.64441100%
9van der Vaart, Aad W. and Jon A. Wellner (1996) Weak Convergence and Empirical Processes: With Applications to Statistics0.64441100%
10Auerbach, Eric, Annie Liang, Max Tabord-Meehan, and Kyohei Okumura (2024) Testing the Fairness-Accuracy Improvability of Algorithms0.64422100%

Showing the top 10 of 57 scored citations.