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A Gaussian Process Framework for Overlap and Causal Effect Estimation with High-Dimensional Covariates

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  • Ghosh Debashis

    (Department of Biostatistics and Informatics, 144805Colorado School of Public Health, 80045Aurora, CO, United States)

  • Cruz Cortés Efrén

    (Department of Biostatistics and Informatics, 144805Colorado School of Public Health, 80045Aurora, CO, United States)

Abstract

A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian random measures as well as reproducing kernel Hilbert space theory. In addition, we propose a strategy for data-adaptive causal effect estimation that does not rely on the strict overlap assumption. These findings reveal under a focused framework the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.

Suggested Citation

  • Ghosh Debashis & Cruz Cortés Efrén, 2019. "A Gaussian Process Framework for Overlap and Causal Effect Estimation with High-Dimensional Covariates," Journal of Causal Inference, De Gruyter, vol. 7(2), pages 1-13, September.
    • Handle: RePEc:bpj:causin:v:7:y:2019:i:2:p:13:n:1
    DOI: 10.1515/jci-2018-0024
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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. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    3. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
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