Imputation and multiple-imputation procedures have been used in practice to handle the problem of ignorable nonresponse in sample surveys. We examine the large-sample properties of these procedures where covariates are available for the case when the complete-data analysis is based on least squares. The results provide a formal justification for the inference procedures discussed by Rubin and Schenker for the location problem and suggest new procedures for the regression problem.
"Asymptotic Results for Multiple Imputation." Ann. Statist. 16 (4) 1550 - 1566, December, 1988. https://doi.org/10.1214/aos/1176351053