Proper and Improper Multiple Imputation

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On the bias of the multiple‐imputation variance estimator in survey sampling (2006, methodology): “Under a parametric model approach, Wang and Robins (1998) and Nielsen (2003) showed that the MI variance estimator for M = ∞ may be biased unless θ̂n is the maximum likelihood estimator of the parameter θ in the imputer’s parametric model.”
Flexible Imputation of Missing Data (2012, background): “Several authors have shown that Rubin’s estimate of the variance is biased (Wang and Robins, 1998; Robins and Wang, 2000; Nielsen, 2003; Kim et al., 2006).”
Inverse Probability Weighting with Missing Predictors of Treatment Assignment or Missingness (2014, background): “Second, as these estimators are not maximum likelihood estimators (MLE), it is not obvious that Rubin’s Rules will apply in this case (Robins and Wang, 2000; Nielsen, 2003).”
Combining Multiple Imputation and Inverse-Probability Weighting (2012, background): “Bias also occurs when IPW is used at stage 1 instead of MI (IPW/MI*), but is smaller than that of MI*/MI*, and indeed of MI*/MI. Theorems 1 and 2 of Robins and Wang (2000) enable the asymptotic (N → ∞) percentage bias in V̂ M to be calculated when M = ∞ (see Web Appendix).”