arXiv 28 May 2026 · Econometrics
arXiv:2605.30609 · PDF · DOI · OpenAlex · Extracted main text
This paper develops a regression framework for the direct estimation of integrated functionals of conditional outcome distributions. The proposed method, termed rectified linear unit (ReLU) regression, projects the ReLU-transformed outcome onto covariates and admits a closed-form estimator. Its population regression function coincides with the integrated conditional distribution function of the outcome, and its convex conjugate, obtained via the Legendre-Fenchel transformation, recovers the integrated conditional quantile function. Both the regression and its conjugate require only mild distributional assumptions and accommodate non-continuous outcomes. We establish the uniform asymptotic distribution of the estimator and develop inference for the conjugate functional via the delta method for Hadamard directionally differentiable maps. Building on these results, we establish identification and inference for average quantile treatment effects over arbitrary subintervals of probability levels. This broadens the set of distributional parameters available to empirical work.
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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 | Chernozhukov, V., I. Fernandez-Val, B. Melly, and K. Wüthrich (2020) Generic inference on quantile and quantile effect functions for discrete outcomes | 0.928 | 5 | 3 | 80% |
| 2 | Fang, Z. and A. Santos (2019) Inference on directionally differentiable functions | 0.855 | 8 | 4 | 62% |
| 3 | Rockafellar, R. T. and S. Uryasev (2000) Optimization of conditional value-at-risk | 0.811 | 4 | 2 | 100% |
| 4 | Dümbgen, L (1993) On nondifferentiable functions and the bootstrap | 0.737 | 3 | 2 | 100% |
| 5 | Ogryczak, W. and A. Ruszczynski (2002) Dual stochastic dominance and related mean-risk models | 0.737 | 3 | 2 | 100% |
| 6 | Rockafellar, R. T. and S. Uryasev (2002) Conditional value-at-risk for general loss distributions | 0.737 | 3 | 2 | 100% |
| 7 | Finkelstein, A., S. Taubman, B. Wright, M. Bernstein, J. Gruber, J.… (2012) The oregon health insurance experiment: Evidence from the first year | 0.644 | 4 | 1 | 100% |
| 8 | Angrist, J., V. Chernozhukov, and I. Fernández-Val (2006) Quantile regression under misspecification, with an application to the U.S wage structure | 0.644 | 2 | 2 | 100% |
| 9 | Beare, B. K. and J. Moon (2015) Transforming Monotone triangular systems | 0.644 | 2 | 2 | 100% |
| 10 | Delgado, M. A. and J. C. Escanciano (2012) Testing the equality of conditional distribution functions in an ordered choice model | 0.644 | 2 | 2 | 100% |
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