Title: What Is a Good Imputation Under MAR Missingness?

Abstract: Missing values pose a persistent challenge in modern data science. Consequently, there is an ever-growing number of publications introducing new imputation methods in various fields. The present paper attempts to take a step back and provide a more systematic analysis: Starting from an in-depth discussion of the Missing at Random (MAR) condition for nonparametric imputation, we first develop an identification result, showing that the widely used Multiple Imputation by Chained Equations (MICE) approach indeed identifies the right conditional distributions. This result, together with two illuminating examples, allows us to propose four essential properties a successful MICE imputation method should meet, thus enabling a more principled evaluation of existing methods and more targeted development of new methods. In particular, we introduce a new method that meets 3 out of the 4 criteria. We then discuss and refine ways to rank imputation methods, even in the challenging setting when the true underlying values are not available. The result is a powerful, easy-to-use scoring algorithm to rank missing value imputations under MAR missingness.