Random Group Variance Estimators for Survey Data with Random Hot Deck Imputation

Random hot deck imputation is often applied to survey data with nonresponse. One of the popular methods for variance estimation without nonresponse is the random group method, which has to be adjusted when it is applied to imputed data. One such kind of adjustment is reimputing nonrespondents in each random group. We show that the random group method with reimputation produces asymptotically unbiased and consistent variance estimators for estimated population totals. As a special case of our general result, the random group variance estimator for the case of no nonresponse is asymptotically unbiased and consistent, a result that has not been documented although the random group method is frequently used in applications. We also show how to apply a shortcut random group method, which reduces the computational complexity due to reimputation, and establish the asymptotic unbiasedness and consistency of the resulting variance estimators.