高维线性模型的扩散自举法
Diffusion Bootstrap for High-Dimensional Linear Models
浏览论文内容
中文总结 AI 辅助
研究高维线性模型中经典自举法的不足，提出基于扩散的配对自举法，通过学习生成律取代经验联合分布，经理论论证和实验验证，该方法能改善方差校准及I型错误校准。
中文摘要 AI 辅助
经典自举法在高维线性模型中表现不佳：配对自举法往往产生过度保守的推断，而残差自举法可能是反保守的，反映出方差校准中的系统性失败。我们提出一种基于扩散的配对自举法，用学习到的生成律取代经验联合分布。在得分近似假设下，我们使用互补的随机微分方程和偏微分方程论证建立了方差一致性。反例表明仅终端W4收敛不足以实现方差一致性。实验表明扩散配对自举法改善了方差校准，通常也改善了I型错误校准，包括在我们理论未涵盖的设置中。
英文摘要
Classical bootstrap methods can behave poorly in high-dimensional linear models: the pairs bootstrap often yields overly conservative inference, whereas the residual bootstrap can be anti-conservative, reflecting systematic failures in variance calibration. We propose a diffusion-based pairs bootstrap that replaces the empirical joint distribution with a learned generative law. We establish variance consistency under a score approximation assumption, using complementary SDE and PDE arguments. Counterexamples show that terminal $W_4$ convergence alone is insufficient for variance consistency. Experiments indicate that diffusion pairs bootstrap improves variance calibration and generally improves Type~I error calibration, including in settings not covered by our theory.
