通过 k-中位数问题进行具有外部效度的实验地点选择
Externally Valid Selection of Experimental Sites via the k-Median Problem
AI总结：
本文将优化外部效度的实验地点选择问题建模为 $k$-中位数问题，证明其与选择最中心协变量向量在最坏情形福利遗憾下近似或精确等价，并通过线性整数规划和两个实证应用验证其优势。
摘要：
我们提出了一种决策论依据，将如何最佳选择实验地点以优化外部效度的问题视为一个 $k$-中位数问题，这是计算机科学和运筹学中一个广受欢迎的问题。我们给出了若干条件，在这些条件下，在所有选择 $k$ 个实验地点的非随机方案中，最小化最坏情形下基于福利的遗憾值，近似等价于——有时恰好等价于——寻找基线地点层面协变量的 $k$ 个最中心向量。$k$-中位数问题可以表述为一个线性整数规划。两个实证应用说明了所建议程序在理论和计算上的优势。
英文摘要：
We present a decision-theoretic justification for viewing the question of how to best choose where to experiment in order to optimize external validity as a $k$-median problem, a popular problem in computer science and operations research. In particular, when treatment effect heterogeneity across experimental and policy-relevant sites is substantial (in a sense we make precise), we present conditions under which minimizing the worst-case, welfare-based regret among all nonrandom schemes that select $k$ sites to experiment is equivalent to solving a $k$-median problem. The connection costs in the relevant $k$-median problem are given by ex-ante bounds on worst-case voltage effects between sites, and minimizing the sum of worst-case voltage effects can be cast as a linear integer program. Two empirical applications illustrate the theoretical and computational benefits of the suggested procedure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
