# Doubly robust inference via calibration

arXiv: https://arxiv.org/abs/2411.02771 · HTML: https://mlsanity.com/paper/2411.02771/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2024.

## Built on by (most cited first, 9 of 9)

- [Stabilized Inverse Probability Weighting via Isotonic Calibration](https://mlsanity.com/paper/2411.06342/) (2024)
- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [Causal Judge Evaluation: Calibrated Surrogate Metrics for LLM Systems](https://mlsanity.com/paper/2512.11150/) (2025)
- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Optimally taming biases in black-box models for efficient semiparametric estimation](https://mlsanity.com/paper/2606.06368/) (2026)
- [Optimal use of a black-box learner in semiparametric estimation](https://mlsanity.com/paper/2607.21541/) (2026)
- [Causal Foundation Models](https://mlsanity.com/paper/2609.03003/) (2026)
- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)
- [Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning](https://mlsanity.com/paper/2608.24858/) (2026)

## Abstract (arXiv)

Doubly robust estimators are widely used for estimating average treatment effects and other linear summaries of regression functions. While consistency requires only one of two nuisance functions to be estimated consistently, asymptotic normality for linear functionals typically requires sufficiently fast convergence of both. We address this mismatch by showing that calibrating the nuisance estimators within a doubly robust procedure can yield doubly robust asymptotic normality. We introduce the idea of calibrated debiased machine learning (DML) and propose a specific implementation in which standard DML is augmented with a simple isotonic regression adjustment. We show that, under a partial orthogonality condition, a calibrated DML estimator remains asymptotically normal if either the regression function or Riesz representer of the functional is estimated sufficiently well, allowing the other to converge arbitrarily slowly or even inconsistently. We also propose a bootstrap-assisted method for constructing confidence intervals, enabling doubly robust inference without additional nuisance estimation. In a range of semi-synthetic benchmark datasets, calibrated DML reduces bias and improves coverage relative to standard DML. Our method can be integrated into existing DML pipelines by adding just a few lines of code to calibrate cross-fitted estimates via isotonic regression.