Abstract An important goal in causal inference is to achieve balance in the covariates among the treatment groups. In this article, we introduce the concept of distributional balance preserving which requires the distribution of the covariates to be the same in different treatment groups. We also introduce a new balance measure called kernel distance, which is the empirical estimate of the probability metric defined in the reproducing kernel Hilbert spaces. Compared to the traditional balance metrics, the kernel distance measures the difference in the two multivariate distributions instead of the difference in the finite moments of the distributions. Simulation results show that the kernel distance is the best indicator of bias in the estimated casual effect compared to several commonly used balance measures. We then incorporate kernel distance into genetic matching, the state-of-the-art matching procedure and apply the proposed approach to analyze the Early Dieting in Girls study. The study indicates that mothers’ overall weight concern increases the likelihood of daughters’ early dieting behavior, but the causal effect is not significant.

中文翻译：

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基于内核的平衡评估指标

摘要 因果推断的一个重要目标是在治疗组之间实现协变量的平衡。在本文中，我们介绍了分布平衡保持的概念，它要求协变量的分布在不同的治疗组中是相同的。我们还引入了一种新的平衡度量，称为核距离，它是在再现核 Hilbert 空间中定义的概率度量的经验估计。与传统的平衡度量相比，核距离衡量的是两个多元分布的差异，而不是分布的有限矩的差异。仿真结果表明，与几种常用的平衡措施相比，核距离是估计偶然效应中偏差的最佳指标。然后，我们将核距离纳入基因匹配中，这是最先进的匹配程序，并应用所提出的方法来分析女孩早期节食研究。研究表明，母亲对体重的整体关注增加了女儿过早节食行为的可能性，但因果关系并不显着。