A note on multiple imputation for method of moments estimation

TL;DR

This paper investigates the limitations of Rubin's variance estimator in multiple imputation when used with method of moments estimation and proposes a new, more accurate variance estimator based on over-imputation.

Contribution

It identifies the asymptotic bias in Rubin's variance estimator for method of moments and introduces a novel over-imputation based estimator for valid inference.

Findings

Rubin's variance estimator is asymptotically biased in this context

The proposed over-imputation variance estimator corrects this bias

Simulation results demonstrate improved inference accuracy

Abstract

Multiple imputation is a popular imputation method for general purpose estimation. Rubin(1987) provided an easily applicable formula for the variance estimation of multiple imputation. However, the validity of the multiple imputation inference requires the congeniality condition of Meng(1994), which is not necessarily satisfied for method of moments estimation. This paper presents the asymptotic bias of Rubin's variance estimator when the method of moments estimator is used as a complete-sample estimator in the multiple imputation procedure. A new variance estimator based on over-imputation is proposed to provide asymptotically valid inference for method of moments estimation.