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Finite-Sample Guarantees for High-Dimensional DML

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  • Victor Quintas-Martinez

Abstract

Debiased machine learning (DML) offers an attractive way to estimate treatment effects in observational settings, where identification of causal parameters requires a conditional independence or unconfoundedness assumption, since it allows to control flexibly for a potentially very large number of covariates. This paper gives novel finite-sample guarantees for joint inference on high-dimensional DML, bounding how far the finite-sample distribution of the estimator is from its asymptotic Gaussian approximation. These guarantees are useful to applied researchers, as they are informative about how far off the coverage of joint confidence bands can be from the nominal level. There are many settings where high-dimensional causal parameters may be of interest, such as the ATE of many treatment profiles, or the ATE of a treatment on many outcomes. We also cover infinite-dimensional parameters, such as impacts on the entire marginal distribution of potential outcomes. The finite-sample guarantees in this paper complement the existing results on consistency and asymptotic normality of DML estimators, which are either asymptotic or treat only the one-dimensional case.

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  • Victor Quintas-Martinez, 2022. "Finite-Sample Guarantees for High-Dimensional DML," Papers 2206.07386, arXiv.org.
    • Handle: RePEc:arx:papers:2206.07386
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    3. Susan Athey & Guido W. Imbens, 2019. "Machine Learning Methods That Economists Should Know About," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 685-725, August.
    4. Athey, Susan & Imbens, Guido W., 2019. "Machine Learning Methods Economists Should Know About," Research Papers 3776, Stanford University, Graduate School of Business.
    5. Victor Chernozhukov & Whitney K. Newey & Victor Quintas-Martinez & Vasilis Syrgkanis, 2021. "Automatic Debiased Machine Learning via Riesz Regression," Papers 2104.14737, arXiv.org, revised Mar 2024.
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