Summary: Hot deck imputation is commonly employed for item nonresponse in sample surveys. It is also a common practice to treat the imputed values as if they are true values, and then compute the variance estimates using standard formulae. This procedure, however, could lead to serious underestimation of the true variance, when the proportion of missing values for an item is appreciable.
We propose a jackknife variance estimator for stratified multistage surveys which is obtained by first adjusting the imputed values for each pseudo-replicate and then applying the standard jackknife formula. The proposed jackknife variance estimator is shown to be consistent as the sample size increases, assuming equal response probabilities within imputation classes and using a particular hot deck imputation.