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August 2022 Doubly robust semiparametric inference using regularized calibrated estimation with high-dimensional data
Satyajit Ghosh, Zhiqiang Tan
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Bernoulli 28(3): 1675-1703 (August 2022). DOI: 10.3150/21-BEJ1378

Abstract

Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a general method for estimating the parameters in the two working models, such that valid Wald confidence intervals can be obtained for the parameter of interest under suitable sparsity conditions if either of the two working models is correctly specified. We propose a computationally tractable two-step algorithm and provide rigorous theoretical analysis which justifies sufficiently fast rates of convergence for the regularized calibrated estimators in spite of sequential construction and establishes a desired asymptotic expansion for the doubly robust estimator. As concrete examples, we discuss applications to partially linear, log-linear, and logistic models and estimation of average treatment effects. Numerical studies in the former three examples demonstrate superior performance of our method, compared with debiased Lasso.

Acknowledgements

The authors would like to thank a referee for constructive comments leading to improvement of the paper. This work was supported in part by PCORI Grant ME-1511-32740.

Citation

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Satyajit Ghosh. Zhiqiang Tan. "Doubly robust semiparametric inference using regularized calibrated estimation with high-dimensional data." Bernoulli 28 (3) 1675 - 1703, August 2022. https://doi.org/10.3150/21-BEJ1378

Information

Received: 1 October 2020; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1378

Keywords: Average treatment effect , calibration estimation , debiased Lasso , double robustness , High-dimensional data , lasso penalty , partially linear model , Semiparametric estimation

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Vol.28 • No. 3 • August 2022
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