Inference with Imputed Conditional Means

In this paper, we develop analytic techniques that can be used to produce appropriate inferences from a data set in which imputation for missing values has been carried out using predictive means. Our derivations are based on asymptotic expansions of point estimators and their associated variance estimators, and the resulting formulas can be thought of as first-order approximations to the estimators that would be used with multiple imputation. The procedures developed can be used either for univariate missing data or for multivariate missing data in which the variables are either missing or observed together, and they are designed for situations in which the complete-data estimator is a smooth function of linear statistics. We illustrate properties of our methods in several examples, including abstract problems as well as applications to large data sets from studies carried out by the federal government.