针对部署重要但难测的群体，优化实验分配以提升评估精度
Target-Weighted Neyman Allocation: Experimental Design for Heterogeneous Treatment Effects under Population Shift
- 两阶段分层设计，根据预估方差分配样本量和处理概率
- 在重要且难测的群体上，可显著提升目标平均处理效应估计精度
- 适用于部署比例未知或有不确定性的场景，鲁棒性强
随机实验常在某一人群进行，以指导另一人群的决策。按实验比例分配会浪费预算于部署中罕见的群体，而按部署比例分配则会低估难以精确测量的群体。本文提出目标加权奈曼分配（TWNA），一种两阶段分层设计，利用试点估计的组别-臂结果方差，来优化最终阶段的样本量与处理概率，以提升目标组平均处理效应（GATE）的估计精度。理想情况下，该规则有闭式解，平衡部署重要性与统计难度；插件规则在试点方差估计稳定后可恢复此最优解。我们还扩展了TWNA以应对部署构成不确定的情况，无论目标分布大致已知或完全未知均保持稳健。最后，我们区分了这种权重鲁棒性与针对偏斜、稀有事件或污染结果的试点鲁棒变体。模拟与真实协变量基准测试表明，当群体同时具备部署重要性和测量困难性时，性能提升最显著。
原文摘要 · Abstract (English)
Randomized experiments are often run in one population to guide decisions in another. Allocating by experimental proportions wastes budget on groups that rarely appear in deployment, whereas allocating by deployment proportions under-samples groups that are hard to measure precisely. We propose \textbf{TWNA} (Target-Weighted Neyman Allocation), a two-stage stratified design that uses pilot estimates of group--arm outcome variances to allocate final-stage sample sizes and treatment probabilities for target-weighted group average treatment effect (GATE) precision. The oracle rule has a closed form and balances deployment importance with statistical difficulty; the plug-in rule recovers it as pilot variance estimates stabilize. We also extend TWNA to handle uncertainty about deployment composition, remaining robust whether the target mix is roughly known or entirely unknown. Finally, we distinguish this weight robustness from a pilot-robust variant for skewed, rare-event, or contaminated outcomes. Simulations and real-covariate benchmarks show the largest gains when groups are both deployment-important and difficult to measure.
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