University of Washington - Department of Statistics
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. The main advantages of imputation estimation are its universality, ease of implementation, and computational efficiency. We illustrate imputation estimators' robustness to model specification on two examples: estimation of genotype frequencies in population genetics and estimation of Markovian evolutionary distances between molecular sequences. In the latter example, using a representative model misspecification, we demonstrate that in non-degenerate cases the imputation estimator dominates the plug-in estimator asymptotically. We conclude by discussing possible strategies for extending the range of applications of imputation estimation.