# Doubly Robust Semiparametric Inference Using Regularized Calibrated Estimation with High-dimensional Data

arXiv: https://arxiv.org/abs/2009.12033 · HTML: https://mlsanity.com/paper/2009.12033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Incorporating External Controls for Estimating the Average Treatment Effect on the Treated with High-Dimensional Data: Retaining Double Robustness and Ensuring Double Safety](https://mlsanity.com/paper/2509.20586/) (2025)

## Abstract (arXiv)

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.