Bootstrap for imputed survey data

Most surveys use imputation to compensate for missing data. However, treating the imputed data set as the complete data set and directly applying existing methods (e.g., the linearization, the jackknife, and the bootstrap) for variance estimation and/or statistical inference does not produce valid results, because these methods do not account for the effect of missing data and/or imputation. In this article we show that correct bootstrap estimates can be obtained by imitating the process of imputing the original data set in the bootstrap resampling; that is, by imputing the bootstrap data sets in exactly the same way that the original data set is imputed. The proposed bootstrap is asymptotically valid irrespective of the sampling design? the imputation method, or the type of statistic used in inference. This enables us to use a unified method in a variety of problems, and in fact this is the only method that works without any restriction on the sampling design, the imputation method, or the type of statistic.