6,623 research outputs found

    Imputation Estimators Partially Correct for Model Misspecification

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    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.Comment: major rewrite, beta-binomial example removed, model based clustering is added to the mixture model example, Bayesian approach is now illustrated with the genetics exampl

    Weak consistency of the 1-nearest neighbor measure with applications to missing data

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    When data is partially missing at random, imputation and importance weighting are often used to estimate moments of the unobserved population. In this paper, we study 1-nearest neighbor (1NN) importance weighting, which estimates moments by replacing missing data with the complete data that is the nearest neighbor in the non-missing covariate space. We define an empirical measure, the 1NN measure, and show that it is weakly consistent for the measure of the missing data. The main idea behind this result is that the 1NN measure is performing inverse probability weighting in the limit. We study applications to missing data and mitigating the impact of covariate shift in prediction tasks
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