用于统计推断和分布鲁棒性的去偏非参数回归
Debiased Nonparametric Regression for Statistical Inference and Distributionally Robustness
- The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种无模型的非参数回归去偏方法，通过加入估计条件期望残差的校正项，使估计量在温和条件下具备风险收敛与渐近正态性，从而支持统计推断并提升协变量偏移下的鲁棒性。
AI中文摘要：
本研究提出了一种针对光滑非参数估计量的去偏方法。尽管随机森林和神经网络等机器学习技术已展现出强大的预测性能，但其理论性质仍相对缺乏充分研究。特别是，许多现代算法缺乏逐点和一致风险收敛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，并且已在 Nadaraya-Watson 回归等经典方法中得到充分确立。为确保各类非参数回归估计量具备这些性质，我们引入了一种无模型去偏方法。通过在初始非参数回归估计量中加入一个校正项，该项估计原始估计量的条件期望残差，或等价地估计其估计误差，我们得到一个去偏估计量；在温和的光滑性条件下，该估计量满足逐点和一致风险收敛，并具有渐近正态性。这些性质促进了统计推断，并增强了对协变量偏移的鲁棒性，使该方法可广泛应用于各类非参数回归问题。
英文摘要：
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.
