Kai Feng, Han Hong, Denis Nekipelov
arXiv 27 Mar 2024 · Econometrics · 1 citations (OpenAlex)
arXiv:2403.18248 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator using tools from geometric measure theory. Building on our Hadamard differentiability results, we apply the functional delta method to obtain the asymptotic properties of the value function process for the binary constrained optimal allocation problem and the plug-in ROC curve estimator. Moreover, the convexity of the optimal allocation value functions facilitates demonstrating the degeneracy of first order derivatives with respect to the policy. We then present a double / debiased estimator for the value functions. Importantly, the conditions that validate Hadamard differentiability justify the margin assumption from the statistical classification literature for the fast convergence rate of plug-in methods.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Audibert, Jean-Yves and Tsybakov, Alexandre B (2007) Fast learning rates for plug-in classifiers | 1.000 | 12 | 3 | 100% |
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| 4 | Devroye, Luc and Györfi, László and Lugosi, Gábor (1996) A Probabilistic Theory of Pattern Recognition | 1.000 | 7 | 3 | 100% |
| 5 | Chernozhukov, Victor and Fernández-Val, Iván and Luo, Ye (2018) The sorted effects method: discovering heterogeneous effects beyond their averages | 0.967 | 21 | 7 | 90% |
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| 9 | Semenova, Vira (2023) Debiased machine learning of set-identified linear models | 0.874 | 5 | 2 | 100% |
| 10 | Luedtke, Alexander R and van der Laan, Mark J (2016) Optimal individualized treatments in resource-limited settings | 0.843 | 3 | 3 | 100% |
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