AI 中文总结
研究两波实验中先导试验对主波设计的影响，提出条件最小最大遗憾（CMR）规则，该规则能在有限样本置信集上最小化最坏情况遗憾，避免可行奈曼分配在小型先导试验中的严重损失，同时获得其在大型先导试验中的大部分收益。
AI 中文摘要
实验者经常进行先导试验，但小型先导试验应在多大程度上塑造主波设计尚无定论。本文展示了有噪声的先导证据应如何在两波实验中指导处理分配概率。两个典型规则代表了极端情况。平衡分配可防范最坏情况，但忽略了某一臂噪声更大的证据。可行的奈曼分配会进行调整，但对于有限的先导试验，它可能对噪声反应过度，导致精度损失任意大。我们提出了一种条件最小最大遗憾（CMR）规则，该规则在处理和控制方差的有限样本置信集上最小化最坏情况遗憾。CMR以高概率保留平衡的最坏情况保护，随着先导试验规模的扩大收敛到奈曼分配，并达到最小最大遗憾率（直至常数）。它扩展到多臂和分层设计，针对四个实地实验进行校准的模拟表明，它避免了可行奈曼分配在小型先导试验中的严重损失，同时获得了其在大型先导试验中的大部分收益。
英文摘要
Experimenters often run pilots, but how much a small pilot should shape the main-wave design has no settled answer. This paper shows how noisy pilot evidence should guide treatment assignment probabilities in two-wave experiments. Two canonical rules mark the extremes. Balanced assignment guards against worst cases but ignores evidence that one arm is noisier. Feasible Neyman allocation adapts, but with a finite pilot it can overreact to noise, producing arbitrarily large precision losses. I propose a Conditional Minimax Regret (CMR) rule that minimizes worst-case regret over a finite-sample confidence set for the treatment and control variances. CMR retains balance's worst-case protection with high probability, converges to the Neyman allocation as the pilot grows, and attains the minimax-regret rate up to constants. It extends to multi-arm and stratified designs, and simulations calibrated to four field experiments show it avoids feasible Neyman's severe small-pilot losses while matching its large-pilot gains.
Comments89 pages, 8 tables; includes online appendix
