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Optimal Nonbipartite Matching and Its Statistical Applications
The American Statistician ( IF 1.8 ) Pub Date : 2011-02-01 , DOI: 10.1198/tast.2011.08294
Bo Lu 1 , Robert Greevy , Xinyi Xu , Cole Beck
Affiliation  

Matching is a powerful statistical tool in design and analysis. Conventional two-group, or bipartite, matching has been widely used in practice. However, its utility is limited to simpler designs. In contrast, nonbipartite matching is not limited to the two-group case, handling multiparty matching situations. It can be used to find the set of matches that minimize the sum of distances based on a given distance matrix. It brings greater flexibility to the matching design, such as multigroup comparisons. Thanks to improvements in computing power and freely available algorithms to solve nonbipartite problems, the cost in terms of computation time and complexity is low. This article reviews the optimal nonbipartite matching algorithm and its statistical applications, including observational studies with complex designs and an exact distribution-free test comparing two multivariate distributions. We also introduce an R package that performs optimal nonbipartite matching. We present an easily accessible web application to make nonbipartite matching freely available to general researchers.

中文翻译:

最优非二分匹配及其统计应用

匹配是设计和分析中强大的统计工具。传统的两组或二部匹配已在实践中广泛使用。然而,它的实用性仅限于更简单的设计。相比之下,非二部匹配不限于两组情况,处理多方匹配情况。它可用于根据给定的距离矩阵找到最小化距离总和的匹配集。它为匹配设计带来了更大的灵活性,例如多组比较。由于计算能力的提高和解决非二分问题的免费算法,计算时间和复杂性方面的成本很低。本文综述了最优非二部匹配算法及其统计应用,包括具有复杂设计的观察性研究和比较两个多变量分布的精确无分布测试。我们还介绍了一个执行最佳非二部匹配的 R 包。我们提供了一个易于访问的 Web 应用程序,使普通研究人员可以免费使用非二部匹配。
更新日期:2011-02-01
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