# Debiased inference for a covariate-adjusted regression function

arXiv: https://arxiv.org/abs/2210.06448 · HTML: https://mlsanity.com/paper/2210.06448/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Continuous Treatment Effects with Surrogate Outcomes](https://mlsanity.com/paper/2402.00168/) (2024)
- [Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data](https://mlsanity.com/paper/2412.19711/) (2024)
- [Double Debiased Machine Learning for Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2503.06156/) (2025)
- [Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression](https://mlsanity.com/paper/2604.13410/) (2026)
- [Causal Generalization of Continuous Treatment Effects under Covariate Shift](https://mlsanity.com/paper/2608.19383/) (2026)

## Abstract (arXiv)

In this article, we study nonparametric inference for a covariate-adjusted regression function. This parameter captures the average association between a continuous exposure and an outcome after adjusting for other covariates. In particular, under certain causal conditions, this parameter corresponds to the average outcome had all units been assigned to a specific exposure level, known as the causal dose-response curve. We propose a debiased local linear estimator of the covariate-adjusted regression function, and demonstrate that our estimator converges pointwise to a mean-zero normal limit distribution. We use this result to construct asymptotically valid confidence intervals for function values and differences thereof. In addition, we use approximation results for the distribution of the supremum of an empirical process to construct asymptotically valid uniform confidence bands. Our methods do not require undersmoothing, permit the use of data-adaptive estimators of nuisance functions, and our estimator attains the optimal rate of convergence for a twice differentiable function. We illustrate the practical performance of our estimator using numerical studies and an analysis of the effect of air pollution exposure on cardiovascular mortality.