A note on reducing the bias of the approximate Bayesian bootstrap imputation variance estimator

Rubin & Schenker (1986) proposed the approximate Bayesian bootstrap, a two-stage resampling procedure, as a method of creating multiple imputations when missing data are ignorable. Kim (2002) showed that the multiple imputation variance estimator is biased for moderate sample sizes when this method is used. To reduce the bias, Kim (2002) proposed modifying the number of samples drawn at the first stage of the Bayesian bootstrap procedure. In this note, we suggest an alternative method for reducing the bias via a simple correction factor applied to the standard multiple imputation variance estimate. The proposed correction is more easily implemented and more efficient than the procedure proposed by Kim (2002).