发表机构
University of California, Berkeley; The Hong Kong University of Science and Technology（加州大学伯克利分校; 香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种无需路径可微性的变分理论，通过条件方差最小化刻画边际积分泛函的最优效率，并给出显式最优权重及交叉拟合估计量，应用于最优策略值、校准误差等，实证显示协方差加权显著降低方差。
AI 中文摘要
在本工作中，我们为半参数效率理论提供了新的视角。具体而言，我们将最优效率及其实现的问题重新表述为一个变分问题：在稳健无偏约束下，最小化估计函数的方差。我们在不要求路径可微性的情况下，为边际积分泛函发展了这一理论。我们研究这样的估计函数：当任意一个指定的干扰分量被错误设定而其他分量正确时，其期望仍等于目标值。我们通过条件方差最小化来刻画其方差的 infimum。对于处理特异性条件均值的仿射函数的最大值，我们获得了显式的最优权重，并构造了交叉拟合估计量，该估计量在关于干扰估计和接近平局的概率的条件下达到该界。对于基于联合观测量的类似最大值，最优权重使用完整的条件协方差矩阵。我们还确定了方差界与经典卷积界一致的条件，该卷积界适用于保持平局至一阶的参数扰动。例子包括最优策略值、$L^1$ 校准误差、Balke--Pearl 界和中介参数。在应用于全国青年男性纵向调查时，协方差加权相对于等权重将交叉拟合估计函数的中位估计方差降低了 12.9%（对于 Balke--Pearl 下端点）和 16.5%（对于上端点），并且在所有 20 次重复交叉拟合分割中均有改进。
英文摘要
In this work, we provide a new perspective on semiparametric efficiency theory. In particular, we reformulate the questions of optimal efficiency and its attainment as a variational problem: minimize variance over estimating functions subject to robust unbiasedness constraints. We develop this theory for marginal-integral functionals without requiring pathwise differentiability. We study estimating functions whose expectations remain equal to the target when any one specified nuisance component is misspecified and the others are correct. We characterize the infimum of their variances through conditional variance minimization. For maxima of affine functions of treatment-specific conditional means, we obtain explicit optimal weights and construct cross-fitted estimators that attain the bound under conditions on nuisance estimation and the probability of near ties. For analogous maxima based on jointly observed quantities, the optimal weights use the full conditional covariance matrix. We also identify conditions under which the variance bound agrees with a classical convolution bound for parametric perturbations that preserve ties to first order. Examples include optimal policy values, $L^1$ calibration error, Balke--Pearl bounds, and mediation parameters. In an application to the National Longitudinal Survey of Young Men, covariance weighting reduces the median estimated variance of the cross-fitted estimating function relative to equal weighting by 12.9% for the lower Balke--Pearl endpoint and 16.5% for the upper, with improvements in all 20 repeated cross-fitting splits.
