Resampling techniques have become increasingly popular for estimation of uncertainty in data collected via surveys. Survey data are also frequently subject to missing data which are often imputed. This note addresses the issue of using resampling methods such as a jackknife or bootstrap in conjunction with imputations that have be sampled stochastically (e.g., in the vein of multiple imputation). It is illustrated that the imputations must be redrawn within each replicate group of a jackknife or bootstrap. Further, the number of multiply imputed datasets per replicate group must dramatically exceed the number of replicate groups for a jackknife. However, this is not the case in a bootstrap approach. A brief simulation study is provided to support the theory introduced in this note.

翻译：重抽样技术已越来越多地用于估算通过调查收集的数据的不确定性。调查数据也常常存在缺失值，这些缺失值通常会被插补。本文探讨了使用刀切法或自助法等重抽样方法配合随机抽样插补（例如，基于多重插补思路）的问题。研究表明，在刀切法或自助法的每个复制组中，必须重新抽取插补数据。此外，对于刀切法，每个复制组中多重插补数据集的数量必须显著超过复制组的数量。然而，在自助法中情况并非如此。本文提供了一项简短的模拟研究，以支持本文提出的理论。