IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2403.15934.html
   My bibliography  Save this paper

Debiased Machine Learning when Nuisance Parameters Appear in Indicator Functions

Author

Listed:
  • Gyungbae Park

Abstract

This paper studies debiased machine learning when nuisance parameters appear in indicator functions. An important example is maximized average welfare under optimal treatment assignment rules. For asymptotically valid inference for a parameter of interest, the current literature on debiased machine learning relies on Gateaux differentiability of the functions inside moment conditions, which does not hold when nuisance parameters appear in indicator functions. In this paper, we propose smoothing the indicator functions, and develop an asymptotic distribution theory for this class of models. The asymptotic behavior of the proposed estimator exhibits a trade-off between bias and variance due to smoothing. We study how a parameter which controls the degree of smoothing can be chosen optimally to minimize an upper bound of the asymptotic mean squared error. A Monte Carlo simulation supports the asymptotic distribution theory, and an empirical example illustrates the implementation of the method.

Suggested Citation

  • Gyungbae Park, 2024. "Debiased Machine Learning when Nuisance Parameters Appear in Indicator Functions," Papers 2403.15934, arXiv.org.
    • Handle: RePEc:arx:papers:2403.15934
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2403.15934
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kitagawa, Toru & Montiel Olea, José Luis & Payne, Jonathan & Velez, Amilcar, 2020. "Posterior distribution of nondifferentiable functions," Journal of Econometrics, Elsevier, vol. 217(1), pages 161-175.
    2. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    3. Timothy B. Armstrong & Michal Kolesár, 2020. "Simple and honest confidence intervals in nonparametric regression," Quantitative Economics, Econometric Society, vol. 11(1), pages 1-39, January.
    4. 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.
    5. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    6. Toru Kitagawa & Aleksey Tetenov, 2018. "Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice," Econometrica, Econometric Society, vol. 86(2), pages 591-616, March.
    7. Victor Chernozhukov & Whitney K Newey & Rahul Singh, 2022. "Debiased machine learning of global and local parameters using regularized Riesz representers [Semiparametric instrumental variable estimation of treatment response models]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 576-601.
    8. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    9. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    10. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    11. Timothy Christensen & Hyungsik Roger Moon & Frank Schorfheide, 2022. "Optimal Decision Rules when Payoffs are Partially Identified," Papers 2204.11748, arXiv.org, revised May 2023.
    12. Vira Semenova, 2020. "Generalized Lee Bounds," Papers 2008.12720, arXiv.org, revised Feb 2023.
    13. Vira Semenova, 2023. "Aggregated Intersection Bounds and Aggregated Minimax Values," Papers 2303.00982, arXiv.org, revised Jun 2024.
    14. Qizhao Chen & Morgane Austern & Vasilis Syrgkanis, 2023. "Inference on Optimal Dynamic Policies via Softmax Approximation," Papers 2303.04416, arXiv.org, revised Dec 2023.
    15. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    16. Hong, Han & Li, Jessie, 2018. "The numerical delta method," Journal of Econometrics, Elsevier, vol. 206(2), pages 379-394.
    17. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    18. Alejandro Sanchez-Becerra, 2023. "Robust inference for the treatment effect variance in experiments using machine learning," Papers 2306.03363, arXiv.org.
    19. Victor Chernozhukov & Whitney K. Newey & Rahul Singh, 2022. "Automatic Debiased Machine Learning of Causal and Structural Effects," Econometrica, Econometric Society, vol. 90(3), pages 967-1027, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kyle Colangelo & Ying-Ying Lee, 2020. "Double Debiased Machine Learning Nonparametric Inference with Continuous Treatments," Papers 2004.03036, arXiv.org, revised Sep 2023.
    2. Ganesh Karapakula, 2023. "Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap," Papers 2301.05703, arXiv.org, revised Jan 2023.
    3. David M. Ritzwoller & Vasilis Syrgkanis, 2024. "Simultaneous Inference for Local Structural Parameters with Random Forests," Papers 2405.07860, arXiv.org, revised Sep 2024.
    4. Zequn Jin & Lihua Lin & Zhengyu Zhang, 2022. "Identification and Auto-debiased Machine Learning for Outcome Conditioned Average Structural Derivatives," Papers 2211.07903, arXiv.org.
    5. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    6. Liu, Lin & Mukherjee, Rajarshi & Robins, James M., 2024. "Assumption-lean falsification tests of rate double-robustness of double-machine-learning estimators," Journal of Econometrics, Elsevier, vol. 240(2).
    7. Zhengyu Zhang & Zequn Jin & Lihua Lin, 2024. "Identification and inference of outcome conditioned partial effects of general interventions," Papers 2407.16950, arXiv.org.
    8. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Stéphane Bonhomme & Martin Weidner, 2020. "Minimizing Sensitivity to Model Misspecification," CeMMAP working papers CWP37/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Stéphane Bonhomme & Martin Weidner, 2022. "Minimizing sensitivity to model misspecification," Quantitative Economics, Econometric Society, vol. 13(3), pages 907-954, July.
    12. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    13. Yuya Sasaki & Takuya Ura & Yichong Zhang, 2022. "Unconditional quantile regression with high‐dimensional data," Quantitative Economics, Econometric Society, vol. 13(3), pages 955-978, July.
    14. Semenova, Vira, 2023. "Debiased machine learning of set-identified linear models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1725-1746.
    15. Susan Athey & Stefan Wager, 2021. "Policy Learning With Observational Data," Econometrica, Econometric Society, vol. 89(1), pages 133-161, January.
    16. Alejandro Sanchez-Becerra, 2023. "Robust inference for the treatment effect variance in experiments using machine learning," Papers 2306.03363, arXiv.org.
    17. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    18. Taisuke Otsu & Mengshan Xu, 2022. "Isotonic propensity score matching," STICERD - Econometrics Paper Series 623, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2020. "Adversarial Estimation of Riesz Representers," Papers 2101.00009, arXiv.org, revised Apr 2024.
    20. Jikai Jin & Vasilis Syrgkanis, 2024. "Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation," Papers 2402.14264, arXiv.org, revised Mar 2024.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2403.15934. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.