单调序贯MAR下完整案例粗化的高效估计及其代价

中文摘要 AI 辅助

完整案例粗化会丢弃部分完整记录中已观测的混杂变量值。我们研究了在单调序贯随机缺失机制下，该方法对具有两个有序、部分观测混杂变量的平均处理效应估计的影响。我们将标准的随机粗化变换专门应用于因果影响函数，建立了典范梯度，并给出了具有序贯多重稳健性的交叉拟合估计量的精确漂移恒等式。在序贯缺失随机和完整案例缺失随机假设同时成立的子模型中，我们将粗化导致的效率损失表示为涉及两个迭代投影的非负期望。当中间混杂变量在第二阶段缺失发生处提供残差信息时，该增益是严格的。Oracle模拟和确定性求积验证了这一效率比较。当第二阶段响应依赖于中间混杂变量时，比较则涉及识别问题：粗化可能引入持续偏差。估计干扰参数模拟包括有界倾向得分设计和高斯应力设计。后者表现出显著的区间覆盖不足，并可能逆转有限样本精度排序，从而限定了效率界在实际中的解释。

英文摘要

Complete-case coarsening discards observed confounder values from partially complete records. We study its consequences for average treatment effect estimation with two ordered, partially observed confounders under monotone sequential missing at random. We specialize the standard coarsening-at-random transformation to the causal influence function, establish the canonical gradient, and give an exact drift identity for a cross-fitted estimator with sequential multiple robustness. In the submodel where both sequential and complete-case missing-at-random assumptions hold, we express the efficiency loss from coarsening as a nonnegative expectation involving two iterated projections. The gain is strict when the intermediate confounder supplies residual information where second-stage missingness occurs. Oracle simulations and deterministic quadrature illustrate this efficiency comparison. When second-stage response depends on the intermediate confounder, the comparison instead concerns identification: coarsening can introduce persistent bias. Estimated-nuisance simulations include a bounded-propensity design and a Gaussian stress design. The latter exhibits substantial interval undercoverage and can reverse the finite-sample precision ordering, qualifying the practical interpretation of the efficiency bound.

发表机构

• University of California, Los Angeles（加州大学洛杉矶分校）

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