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

TL;DR

This paper introduces a regularized calibrated estimation method for high-dimensional semiparametric models, enabling valid inference for low-dimensional parameters even with model misspecification, supported by theoretical guarantees and numerical evidence.

Contribution

It develops a novel regularized calibrated estimation approach for high-dimensional doubly robust inference, with a computationally feasible algorithm and rigorous theoretical validation.

Findings

Method achieves valid confidence intervals under sparsity.

Outperforms debiased Lasso in simulations.

Applicable to various models including treatment effect estimation.

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.