Résumé
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 fully conditional specification (FCS) approach indeed identifies the
correct conditional distributions. Based on this analysis, we propose three
essential properties an ideal 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 imputation method, denoted
mice-DRF, that meets two out of the three criteria. We also discuss ways to
compare imputation methods, based on distributional distances. Finally,
numerical experiments illustrate the points made in this discussion.