Missing data is a nuisance in statistics. Real donor imputation can be used with item nonresponse. A pool of donor units with similar values on auxiliary variables is matched to each unit with missing values. The missing value is then replaced by a copy of the corresponding observed value from a randomly drawn donor. Such methods can to some extent protect against nonresponse bias. But bias also depends on the estimator and the nature of the data. We adopt techniques from kernel estimation to combat this bias. Motivated by Pólya urn sampling, we sequentially update the set of potential donors with units already imputed, and use multiple imputations via Bayesian bootstrap to account for imputation uncertainty. Simulations with a single auxiliary variable show that our imputation method performs almost as well as competing methods with linear data, but better when data is nonlinear, especially with large samples.

Real donor matching is associated with hot deck imputation. Aux-iliary variables are used to match donee units with missing values to aset of donor units with observed values, and the donee missing valuesare ‘replaced’ by copies of the donor values, as to create completelyfilled in datasets. The matching of donees and donors is complicatedby the fact that the observed sample survey data is often both sparseand bounded. The important choice of how many possible donors tochoose from involves a trade-off between bias and variance. We trans-fer concepts from kernel estimators to real donor imputation. In asimulation study we show how bias, variance and the estimated vari-ance of a population behaves, focusing on the size of donor pools.