Imputation for missing values and corresponding variance estimation

Imputation is commonly used to compensate for missing data in surveys. We consider the general case where the responses on either the variable of interest y or the auxiliary variable x or both may be missing. We use ratio imputation for y when the associated x is observed and different imputations when x is not observed. We obtain design‐consistent linearization and jackknife variance estimators under uniform response. We also report the results of a simulation study on the efficiencies of imputed estimators, and relative biases and efficiencies of associated variance estimators.