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Debiased Machine Learning of Set-Identified Linear Models

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  • Vira Semenova

Abstract

This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the boundary and propose a multiplier bootstrap procedure to conduct inference. I apply this result to the partially linear model, the partially linear IV model and the average partial derivative with an interval-valued outcome.

Suggested Citation

  • Vira Semenova, 2017. "Debiased Machine Learning of Set-Identified Linear Models," Papers 1712.10024, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:1712.10024
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    3. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    4. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    5. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers 43/12, Institute for Fiscal Studies.
    6. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    7. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey, 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects," American Economic Review, American Economic Association, vol. 107(5), pages 261-265, May.
    8. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
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