Inference for domains under imputation for missing survey data

The authors study the estimation of domain totals and means under survey-weighted regression imputation for missing items. They use two different approaches to inference: (i) design-based with uniform response within classes; (ii) model-assisted with ignorable response and an imputation model. They show that the imputed domain estimators are biased under (i) but approximately unbiased under (ii). They obtain a bias-adjusted estimator that is approximately unbiased under (i) or (ii). They also derive linearization variance estimators. They report the results of a simulation study on the bias ratio and efficiency of alternative estimators, including a complete case estimator that requires the knowledge of response indicators.