Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator for finite‐population inference using a superpopulation model framework. We also clarify conditions for its robustness. For variance estimation, the conventional bootstrap inference is invalid for matching estimators with a fixed number of matches due to the nonsmoothness nature of the matching estimator. We propose a new replication variance estimator, which is asymptotically valid. The key strategy is to construct replicates directly based on the linear terms of the martingale representation for the matching estimator, instead of individual records of variables. Simulation studies confirm that the proposed method provides valid inference.

中文翻译：

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渐进理论和预测式均值匹配归因的超人口模型框架

预测均值匹配插补在处理抽样调查中的项目无响应时很流行。在本文中，我们使用超级人口模型框架研究了用于有限人口推断的预测均值匹配估计量的渐近性质。我们还阐明了其健壮性的条件。对于方差估计，由于匹配估计器的非平滑性，常规的自举推断对于具有固定数目的匹配的匹配估计器无效。我们提出了一个新的复制方差估计量，它是渐近有效的。关键策略是根据匹配估计量的the表示形式的线性项直接构建复制项，而不是单独的变量记录。仿真研究证实了该方法提供了有效的推论。