On the Stationary Distribution of Iterative Imputations

TL;DR

This paper analyzes the stationary distributions of iterative imputation methods, showing conditions for convergence to Bayesian posteriors and establishing consistency even with incompatible models.

Contribution

It provides theoretical conditions under which iterative imputations converge to Bayesian posteriors or remain consistent despite incompatibility.

Findings

Imputation distribution converges to Bayesian posterior under compatibility.

Incompatible but valid models still yield consistent estimators.

Provides sufficient conditions for convergence in total variation.

Abstract

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties. More precisely, when the conditional models are compatible (defined in the text), we give a set of sufficient conditions under which the imputation distribution converges in total variation to the posterior distribution of a Bayesian model. When the conditional models are incompatible but are valid, we show that the combined imputation estimator is consistent.