Design and analysis of bipartite experiments under a linear exposure-response model

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY Electronic Journal of Statistics Pub Date : 2023-01-01 DOI:10.1214/23-ejs2111
Christopher Harshaw, Fredrik Sävje, David Eisenstat, Vahab Mirrokni, Jean Pouget-Abadie
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引用次数: 1

Abstract

A bipartite experiment consists of one set of units being assigned treatments and another set of units for which we measure outcomes. The two sets of units are connected by a bipartite graph, governing how the treated units can affect the outcome units. In this paper, we consider estimation of the average total treatment effect in the bipartite experimental framework under a linear exposure-response model. We introduce the Exposure Reweighted Linear (ERL) estimator, and show that the estimator is unbiased, consistent and asymptotically normal, provided that the bipartite graph is sufficiently sparse. To facilitate inference, we introduce an unbiased and consistent estimator of the variance of the ERL point estimator. Finally, we introduce a cluster-based design, Exposure-Design, that uses heuristics to increase the precision of the ERL estimator by realizing a desirable exposure distribution.
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线性暴露-响应模型下的二部实验设计与分析
一个双部分实验包括一组被分配治疗的单位和另一组我们测量结果的单位。这两组单元通过二部图连接起来,控制处理单元如何影响结果单元。在线性暴露-响应模型下,我们考虑在二部实验框架下的平均总处理效果的估计。我们引入了曝光重加权线性(ERL)估计量,并证明了在二部图足够稀疏的条件下,该估计量是无偏的、一致的和渐近正态的。为了便于推理,我们引入了ERL点估计量方差的无偏一致估计量。最后,我们介绍了一种基于聚类的设计,曝光设计,它使用启发式方法通过实现理想的曝光分布来提高ERL估计器的精度。
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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
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