Inference with Imputed Conditional Means

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Calculating Comparable Statistics From Incomparable Surveys, With an Application to Poverty in India (2004, methodology): “Schenker (2003) calculated standard errors for the bridged estimates adapting a methodology developed by Schafer and Schenker (2000).”
Missing data: our view of the state of the art. (2002, methodology): “…values of Y. Replacing Y with Y ˆ is called conditional mean imputation, because Y ˆ estimates the conditional mean of Y given X. Conditional mean imputation is nearly optimal for a limited class of estimation problems if special corrections are made to standard errors (Schafer & Schenker, 2000).”
Flexible Imputation of Missing Data (2012, methodology): “Various methods have been proposed to correct the variance (Lee et al., 1994; Fay, 1996; Rao, 1996; Schafer and Schenker, 2000).”
A comparison of multiple imputation and doubly robust estimation for analyses with missing data (2006, background): “Multiple imputation is computationally straightforward if all the variables are continuous, but it may not give sensible answers if methods for continuous data are applied to discrete, especially categorical, variables, particularly if the probabilities are extreme (Schafer and Schenker, 2000). Furt”