发表机构
University of Ottawa; McGill University; University of Neuchâtel（渥太华大学; 麦吉尔大学; 纳沙泰尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种学习器不可知的模型辅助估计框架，通过交叉拟合和条件加权实现设计无偏与渐近最优，并验证其有限样本性能。
AI 中文摘要
模型辅助估计利用预测规则来提高有限总体参数估计的效率，同时保留基于设计的推断。尽管已考虑了灵活的预测方法，但现有的理论结果大多针对特定方法。我们开发了一个学习器不可知的框架，用关于抽样设计和预测误差的一般条件取代了对单个学习器的单独分析。我们将设计感知和设计不可知的交叉拟合联系起来，并刻画了使它们在折间产生条件独立性的抽样设计。在适当条件下，条件加权给出精确的设计无偏性。我们建立了与神谕估计量的一阶等价性，从而得到设计一致性和渐近正态性，并阐明了条件包含概率和原始包含概率何时产生相同的一阶行为。我们提出了基于交叉拟合残差的一致方差估计量，并构造了渐近有效的置信区间。在额外的模型和正则性条件下，我们通过达到Godambe-Joshi下界建立了渐近最优性。模拟表明，交叉拟合显著减少了有限样本偏差，并改善了自适应学习器的方差估计和覆盖率。
英文摘要
Model-assisted estimation uses prediction rules to improve the efficiency of estimators of finite population parameters while retaining design-based inference. Although flexible prediction methods have been considered, existing theoretical results are largely method-specific. We develop a learner-agnostic framework that replaces separate analyses for individual learners with general conditions on the sampling design and prediction error. We connect design-aware and design-agnostic cross-fitting and characterize the sampling designs under which they yield conditional independence across folds. Under suitable conditions, conditional weighting gives exact design-unbiasedness. We establish first-order equivalence to oracle estimators, leading to design consistency and asymptotic normality, and clarify when conditional and original inclusion probabilities yield the same first-order behavior. We propose consistent variance estimators based on cross-fitted residuals and construct asymptotically valid confidence intervals. Under additional model and regularity conditions, we establish asymptotic optimality through attainment of the Godambe--Joshi lower bound. Simulations show that cross-fitting substantially reduces finite-sample bias and improves variance estimation and coverage with adaptive learners.
