When Does Inexact Matching Ensure Balance and Inference without Adjustment?
非精确匹配何时能在无需调整的情况下保证平衡与有效推断？AI 解读 ↓
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非精确匹配何时能在无需调整的情况下保证平衡与有效推断？
- 研究问题
- 连续协变量下，一对一不放回匹配的残余不平衡何时可以忽略，从而支持无需额外调整的处理效应推断？
- 方法与思路
- 作者研究采用二次协变量距离目标的匹配，分析光滑函数族上的平均差异，并考察多类处理效应及配对随机化推断。
- 材料陈述的贡献
- 摘要称，满足所述条件且维数不超过三时，不平衡相对根号样本量尺度可忽略；四维及更高维反例揭示适用边界。
- 阅读关注点
- 核对倾向得分与局部对照充足性的具体条件、光滑函数限制，以及各类效应的方差估计、自助法和随机化推断条件。
- 阅读边界
- 仅据 arXiv 第1版预印本摘要，不能据此确认同行评审或期刊接收。摘要未列出完整条件；配对随机化推断的有效性限于所述超总体意义。
原文摘要
One-to-one matching without replacement is a classical approach to constructing comparable treated and control samples in the design of observational studies. It pairs each treated unit with a distinct control while minimizing a covariate distance objective. With continuous covariates, the matched pairs generally remain inexact, which contributes to bias in downstream analysis. Its key theoretical properties, such as the resulting imbalance between matched pairs and when it is negligible to support valid inference, remain unclear. In this paper, we analyze one-to-one matching based on $d$-dimensional, continuous covariates with a quadratic covariate-distance objective. First, we find that when $d\leq 3$, under standard conditions on the propensity score ensuring abundant control samples near each treated sample, the imbalance (difference between within-group averages) is root-$n$ negligible uniformly over the family of smooth functions with a common first- and second-order derivative bound. However, such balance is subject to a dimension restriction, as we construct examples in which the imbalance is root-$n$ non-negligible when $d=4$ and dominates root-$n$ rate when $d>4$. Second, we show that when $d\leq 3$, the matched design allows valid Wald-type and bootstrap inference for the average treatment effect on the treated, distributional treatment effects, and quantile treatment effects. Thus, the same outcome-blind matched design supports various downstream inferences without having to tailor the design to the targets. Finally, paired randomization inference based on the matched design is asymptotically valid in the super-population sense for $d\leq 3$ but can fail when $d=4$. We corroborate the theoretical results with numerical experiments.