Imputation Estimators Partially Correct for Model Misspecification

TL;DR

This paper demonstrates that simple imputation estimators can offer partial robustness against model misspecification across various inference problems, outperforming traditional plug-in estimates in certain cases.

Contribution

It introduces the concept that imputation estimators can partially correct for model misspecification and illustrates this robustness through multiple practical examples.

Findings

Imputation estimators provide partial protection against model misspecification.

In non-degenerate cases, imputation estimators outperform plug-in estimates asymptotically.

The paper outlines a Bayesian implementation of the imputation-based estimation.

Abstract

Inference problems with incomplete observations often aim at estimating population properties of unobserved quantities. One simple way to accomplish this estimation is to impute the unobserved quantities of interest at the individual level and then take an empirical average of the imputed values. We show that this simple imputation estimator can provide partial protection against model misspecification. We illustrate imputation estimators' robustness to model specification on three examples: mixture model-based clustering, estimation of genotype frequencies in population genetics, and estimation of Markovian evolutionary distances. In the final example, using a representative model misspecification, we demonstrate that in non-degenerate cases, the imputation estimator dominates the plug-in estimate asymptotically. We conclude by outlining a Bayesian implementation of the imputation-based estimation.