An Approximation Algorithm for Blocking of an Experimental Design
实验设计分块的近似算法AI 解读 ↓
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实验设计分块的近似算法
- 研究问题
- 当实验单位需要组成大小相等且超过两人的同质区组时，如何兼顾计算可行性、分块质量与平均处理效应估计误差控制？
- 方法与思路
- 作者提出多项式时间近似分块方法，以最小化区组内所有单位两两差异的最大值，并分析其与处理效应估计误差的关系。
- 材料陈述的贡献
- 摘要称，算法有接近最优分块的保证，模拟中的同质性表现更好；控制最大差异可对所有处理分配约束估计误差。
- 阅读关注点
- 应核对单位差异的定义、近似保证的具体界限、差异如何转化为结果误差，以及模拟比较的设计与参照算法。
- 阅读边界
- 仅据所给 Crossref 摘要，近似比例及误差界条件未说明；模拟优势限于作者报告的情形，不能推广为所有实验设计中的优势。
原文摘要
Abstract Blocked randomized designs are used to improve the precision of treatment effect estimates compared to a completely randomized design. A block is a set of units that are relatively homogeneous and consequently would tend to produce relatively similar outcomes if the treatment had no effect. The problem of finding the optimal blocking of the units into equal sized blocks of any given size larger than two is known to be a difficult problem—there is no polynomial time method guaranteed to find the optimal blocking. All available methods to solve the problem are heuristic methods. We propose methods that run in polynomial time and guarantee a blocking that is provably close to the optimal blocking. In all our simulation studies, the proposed methods perform better, create better homogeneous blocks, compared with the existing methods. Our blocking method aims to minimize the maximum of all pairwise differences of units in the same block. We show that bounding this maximum difference ensures that the error in the average treatment effect estimate is similarly bounded for all treatment assignments. In contrast, if the blocking bounds the average or sum of these differences, the error in the average treatment effect estimate can still be large in several treatment assignments.