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June 2022 Doubly debiased lasso: High-dimensional inference under hidden confounding
Zijian Guo, Domagoj Ćevid, Peter Bühlmann
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Ann. Statist. 50(3): 1320-1347 (June 2022). DOI: 10.1214/21-AOS2152

Abstract

Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected by hidden confounding and propose the doubly debiased lasso estimator for individual components of the regression coefficient vector. Our advocated method simultaneously corrects both the bias due to estimation of high-dimensional parameters as well as the bias caused by the hidden confounding. We establish its asymptotic normality and also prove that it is efficient in the Gauss–Markov sense. The validity of our methodology relies on a dense confounding assumption, that is, that every confounding variable affects many covariates. The finite sample performance is illustrated with an extensive simulation study and a genomic application. The method is implemented by the DDL package available from CRAN.

Funding Statement

The research of Z. Guo was supported in part by the NSF Grants DMS-1811857, 2015373 and NIH-1R01GM140463-01; Z. Guo also acknowledges financial support for visiting the Institute of Mathematical Research (FIM) at ETH Zurich.
D. Ćevid and P. Bühlmann received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 786461).

Acknowledgments

We thank Yuansi Chen for providing the code to preprocess the raw data from the GTEx project. We also thank Matthias Löffler for his help and useful discussions about random matrix theory.

Z. Guo and D. Ćevid contributed equally to this work.

Citation

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Zijian Guo. Domagoj Ćevid. Peter Bühlmann. "Doubly debiased lasso: High-dimensional inference under hidden confounding." Ann. Statist. 50 (3) 1320 - 1347, June 2022. https://doi.org/10.1214/21-AOS2152

Information

Received: 1 October 2020; Revised: 1 November 2021; Published: June 2022
First available in Project Euclid: 16 June 2022

Digital Object Identifier: 10.1214/21-AOS2152

Subjects:
Primary: 62E20 , 62F12
Secondary: 62J07

Keywords: Causal inference , dense confounding , linear model , spectral deconfounding , structural equation model

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 3 • June 2022
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