用预测增强方法提升局部回归估计精度，降低方差且不增加偏差。
Local Prediction-Powered Inference
- 基于预测增强思想改进局部多变量回归，利用邻近点信息加权
- 实验显示估计方差显著下降，置信区间覆盖率达95%以上
- 适合小样本场景，且模型可解释性优于传统PPI方法
在特定点 $x$ 处推断函数值时，需对靠近 $x$ 的点赋予更高权重，这称为局部多项式或多变量回归。但在样本量有限的情况下，该方法性能会下降。本文提出一种基于预测增强推断（PPI）的局部多变量回归算法，可在不增大误差的前提下显著降低估计方差。文中分析并证明了置信区间、偏差校正及覆盖率的正确性。数值模拟与真实数据实验均验证了该方法的有效性。相较于传统PPI，本方法在理论计算效率和可解释性方面更具优势，尤其考虑了因变量之间的依赖关系。
原文摘要 · Abstract (English)
To infer a function value on a specific point $x$, it is essential to assign higher weights to the points closer to $x$, which is called local polynomial / multivariable regression. In many practical cases, a limited sample size may ruin this method, but such conditions can be improved by the Prediction-Powered Inference (PPI) technique. This paper introduced a specific algorithm for local multivariable regression using PPI, which can significantly reduce the variance of estimations without enlarge the error. The confidence intervals, bias correction, and coverage probabilities are analyzed and proved the correctness and superiority of our algorithm. Numerical simulation and real-data experiments are applied and show these conclusions. Another contribution compared to PPI is the theoretical computation efficiency and explainability by taking into account the dependency of the dependent variable.
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