发表机构
Division of Biostatistics; School of Public Health, University of California, Berkeley（生物统计分部; 加州大学伯克利分校公共卫生学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展半参数卷积定理至方向性路径可微泛函，刻画正则性条件、效率界及影响函数，并应用于处理值、工具变量界和校准，建立有限分层模型中的可行可达性。
AI 中文摘要
经典半参数卷积定理刻画了路径可微参数的正则估计量的极限分布。我们将此分析扩展到方向性路径可微泛函。沿子空间或凸锥的正则性迫使方向导数在该处与一个有界线性泛函一致，并且每个此类估计量都有一个由该泛函确定的高斯卷积因子。我们刻画了相关子空间，比较了它们的效率界，并识别了有效估计量的影响函数。这些比较表明，更强的正则性要求何时会提高方差界。在可加性条件下，高斯极限实验分解为一个线性估计问题和一个非线性问题。在平方误差下，它们的极小极大风险相加；对于更一般的损失，高斯分量通过损失的卷积进入。对处理值、工具变量界和校准的应用给出了显式的有效影响函数，比较了现有程序，并建立了在有限分层模型中的可行可达性。
英文摘要
The classical semiparametric convolution theorem characterizes the limiting distributions of regular estimators of pathwise differentiable parameters. We extend this analysis to directionally pathwise differentiable functionals. Regularity along a subspace or convex cone forces the directional derivative to agree there with a bounded linear functional, and every such estimator has a Gaussian convolution factor determined by that functional. We characterize the relevant subspaces, compare their efficiency bounds, and identify the influence functions of efficient estimators. These comparisons show when a stronger regularity requirement increases the variance bound. Under an additivity condition, the Gaussian limit experiment separates into a linear estimation problem and a nonlinear one. Their minimax risks add under squared error; for more general losses, the Gaussian component enters through convolution of the loss. Applications to treatment values, instrumental-variable bounds, and calibration give explicit efficient influence functions, compare existing procedures, and establish feasible attainment in finite-stratum models.
