arXiv 13 Jun 2025 · Statistics — Methodology
arXiv:2506.12215 · PDF · DOI · OpenAlex · Extracted main text
Many important quantities of interest are only partially identified from observable data: the data can limit them to a set of plausible values, but not uniquely determine them. This paper develops a unified framework for covariate-assisted estimation, inference, and decision making in partial identification problems where the parameter of interest satisfies a series of linear constraints, conditional on covariates. In such settings, bounds on the parameter can be written as expectations of solutions to conditional linear programs that optimize a linear function subject to linear constraints, where both the objective function and the constraints may depend on covariates and need to be estimated from data. Examples include estimands involving the joint distributions of potential outcomes, policy learning with inequality-aware value functions, and instrumental variable settings. We propose two de-biased estimators for bounds defined by conditional linear programs. The first directly solves the conditional linear programs with plugin estimates and uses output from standard LP solvers to de-bias the plugin estimate, avoiding the need for computationally demanding vertex enumeration of all possible solutions for symbolic bounds. The second uses entropic regularization to create smooth approximations to the conditional linear programs, trading a small amount of approximation error for improved estimation and computational efficiency. We establish conditions for asymptotic normality of both estimators, show that both estimators are robust to first-order errors in estimating the conditional constraints and objectives, and construct Wald-type confidence intervals for the partially identified parameters. These results also extend to policy learning problems where the value of a decision policy is only partially identified. We apply our methods to a study on the effects of Medicaid enrollment.
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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 | Levis, A. W., Bonvini, M., Zeng, Z., Keele, L., and Kennedy, E. H (2023) Covariate-assisted bounds on causal effects with instrumental variables | 0.843 | 5 | 3 | 60% |
| 2 | Semenova, V (2024) Aggregated Intersection Bounds and Aggregated Minimax Values | 0.737 | 3 | 2 | 100% |
| 3 | Weed, J (2018) An explicit analysis of the entropic penalty in linear programming | 0.693 | 6 | 2 | 50% |
| 4 | D'Adamo, R (2023) Orthogonal Policy Learning Under Ambiguity | 0.644 | 2 | 2 | 100% |
| 5 | Ji, W., Lei, L., and Spector, A (2024) Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects | 0.644 | 2 | 2 | 100% |
| 6 | Pu, H. and Zhang, B (2021) Estimating optimal treatment rules with an instrumental variable: A partial identification learning approach | 0.511 | 2 | 2 | 50% |
| 7 | Ben-Michael, E., Imai, K., and Jiang, Z (2024) Policy Learning with Asymmetric Counterfactual Utilities self | 0.511 | 2 | 2 | 50% |
| 8 | Audibert, J. Y. and Tsybakov, A. B (2007) Fast learning rates for plug-in classifiers | 0.405 | 1 | 1 | 100% |
| 9 | Cui, Y (2021) Individualized decision making under partial identification: three perspectives, two optimality results, and one paradox | 0.405 | 1 | 1 | 100% |
| 10 | Han, S (2021) Optimal Dynamic Treatment Regimes and Partial Welfare Ordering | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding | 0.405 | 1 | 1 |
| 2 | On the Lower Confidence Band for the Optimal Welfare in Policy Learning | 0.405 | 1 | 1 |