On the performance of bias–reduction techniques for variance estimation in approximate Bayesian bootstrap imputation

Multiply imputed data sets can be created with the approximate Bayesian bootstrap (ABB) approach under the assumption of ignorable nonresponse. The theoretical development and inferential validity are predicated upon asymptotic properties; and biases are known to occur in small-to-moderate samples. There have been attempts to reduce the finite-sample bias for the multiple imputation variance estimator. In this note, we present an empirical study for evaluating the comparative performance of the two proposed bias–correction techniques and their impact on precision. The results suggest that to varying degrees, bias improvements are outweighed by efficiency losses for the variance estimator. We argue that the original ABB has better small-sample properties than the modified versions in terms of the integrated behavior of accuracy and precision, as measured by the root mean-square error.