Nan Liu, Yanbo Liu, Yuya Sasaki, Yuanyuan Wan
arXiv 18 Nov 2025 · Econometrics
arXiv:2511.14700 · PDF · Extracted main text
We develop methods for nonparametric uniform inference in cost-sensitive binary classification, a framework that encompasses maximum score estimation, predicting utility maximizing actions, and policy learning. These problems are well known for slow convergence rates and non-standard limiting behavior, even under point identified parametric frameworks. In nonparametric settings, they may further suffer from failures of identification. To address these challenges, we introduce a strictly convex surrogate loss that point-identifies a representative nonparametric policy function. We then estimate this representative policy function to conduct inference on both the optimal classification policy and the optimal policy value. This approach enables Gaussian inference, substantially simplifying empirical implementation relative to working directly with the original classification problem. In particular, we establish root-$n$ asymptotic normality for the optimal policy value and derive a Gaussian approximation for the optimal classification policy at the standard nonparametric rate. Extensive simulation studies corroborate the theoretical findings. We apply our method to the National JTPA Study to conduct inference on the optimal treatment assignment policy and its associated welfare.
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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 | Athey, S. and S. Wager (2021) Policy learning with observational data | 1.000 | 5 | 3 | 100% |
| 2 | Manski, C. F (1975) Maximum score estimation of the stochastic utility model of choice | 1.000 | 5 | 3 | 100% |
| 3 | Manski, C. F (1985) Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator | 1.000 | 5 | 3 | 100% |
| 4 | Kitagawa, T. and A. Tetenov (2018) Who should be treated? empirical welfare maximization methods for treatment choice | 0.974 | 13 | 5 | 92% |
| 5 | Elliott, G. and R. P. Lieli (2013) Predicting binary outcomes | 0.928 | 4 | 3 | 100% |
| 6 | Mbakop, E. and M. Tabord-Meehan (2021) Model selection for treatment choice: Penalized welfare maximization | 0.874 | 7 | 2 | 100% |
| 7 | Kim, J. and D. Pollard (1990) Cube root asymptotics | 0.811 | 4 | 2 | 100% |
| 8 | Bartlett, P. L., M. I. Jordan, and J. D. McAuliffe (2006) Convexity, classification, and risk bounds | 0.737 | 3 | 2 | 100% |
| 9 | Bhattacharya, D. and P. Dupas (2012) Inferring welfare maximizing treatment assignment under budget constraints | 0.737 | 3 | 2 | 100% |
| 10 | Kitagawa, T., S. Sakaguchi, and A. Tetenov (2023) Constrained classification and policy learning | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 68 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | 2606.01659 | 0.644 | 2 | 2 |
| 2 | Root-$n$ Asymptotically Normal Maximum Score Estimation | 0.511 | 2 | 1 |