提出一种无需模型假设的去偏方法，让机器学习回归模型具备统计推断能力。
Debiased Nonparametric Regression for Statistical Inference and Distributionally Robustness
- 通过添加估计误差修正项，对非参数回归器进行去偏处理。
- 在弱光滑条件下实现点态与一致风险收敛及渐近正态性。
- 适用于随机森林、神经网络等模型，提升对变量分布变化的鲁棒性。
本研究提出一种针对平滑非参数估计器的去偏方法。尽管随机森林、神经网络等机器学习技术具有出色的预测性能，但其理论性质仍相对不足，许多现代算法缺乏点态和一致风险收敛性以及渐近正态性的保证。这些性质对于统计推断和稳健估计至关重要，而经典方法如Nadaraya-Watson回归已能良好满足。为使多种非参数回归估计器具备这些性质，本文引入一种无需模型假设的去偏方法：通过在原始非参数回归估计器中加入一个估计条件期望残差（即估计误差）的修正项，得到去偏估计器。在弱光滑条件下，该方法可保证点态与一致风险收敛，以及渐近正态性，从而支持统计推断，并增强对协变量偏移的鲁棒性，广泛适用于各类非参数回归问题。
原文摘要 · Abstract (English)
This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain relatively underexplored. In particular, many modern algorithms lack guarantees of pointwise and uniform risk convergence, as well as asymptotic normality. These properties are essential for statistical inference and robust estimation and have been well-established for classical methods such as Nadaraya-Watson regression. To ensure these properties for various nonparametric regression estimators, we introduce a model-free debiasing method. By incorporating a correction term that estimates the conditional expected residual of the original estimator, or equivalently, its estimation error, into the initial nonparametric regression estimator, we obtain a debiased estimator that satisfies pointwise and uniform risk convergence, along with asymptotic normality, under mild smoothness conditions. These properties facilitate statistical inference and enhance robustness to covariate shift, making the method broadly applicable to a wide range of nonparametric regression problems.
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