Doubly debiased lasso: High-dimensional inference under hidden confounding
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Date
2022-06
Publication Type
Journal Article
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yes
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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.
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published
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Journal / series
Volume
50 (3)
Pages / Article No.
1320 - 1347
Publisher
Institute of Mathematical Statistics
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Subject
Causal inference; structural equation model; dense confounding; linear model; spectral deconfounding
Organisational unit
03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
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Funding
786461 - Statistics, Prediction and Causality for Large-Scale Data (EC)