I have been looking at the literature of missing data problems. Many of them talks about multiple imputation, but I'm just interested in what bias occur and how to correct the bias if we employ a regression imputation, i.e. impute the missing values in that column using lienar regression based on the complete data.
But so far I haven't find any literature talking about theoretical analysis on such imputation strategy.
In Statistical Analysis with Missing Data 3rd edition by Little and Rubin Ch4.2.2 page 70, they mentioned regression imputation as an example of conditional mean imputation. But there is no analysis about bias, variance, bias correction introduced.
Thank you for any advice on such resources.