# Debiased Regression for Root-N-Consistent Conditional Mean Estimation

arXiv: https://arxiv.org/abs/2411.11748 · HTML: https://mlsanity.com/paper/2411.11748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 5 of 5)

- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Semi-parametric efficiency bounds for high-dimensional models](https://mlsanity.com/paper/1601.00815/) (2016)
- [Policy design in experiments with unknown interference](https://mlsanity.com/paper/2011.08174/) (2020)

## Abstract (arXiv)

This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a data-driven manner with minimal assumptions; however, these methods typically fail to achieve √n-consistency in their convergence rates, and many, including those in machine learning, lack guarantees that their estimators asymptotically follow a normal distribution. To address these challenges, we propose a debiasing technique for nonparametric estimators by adding a bias-correction term to the original estimators, extending the conventional one-step estimator used in semiparametric analysis. Specifically, for each data point, we estimate the conditional expected residual of the original nonparametric estimator, which can, for instance, be computed using kernel (Nadaraya-Watson) regression, and incorporate it as a bias-reduction term. Our theoretical analysis demonstrates that the proposed estimator achieves √n-consistency and asymptotic normality under a mild convergence rate condition for both the original nonparametric estimator and the conditional expected residual estimator. Notably, this approach remains model-free as long as the original estimator and the conditional expected residual estimator satisfy the convergence rate condition. The proposed method offers several advantages, including improved estimation accuracy and simplified construction of confidence intervals.