Imprecise Imputation: A Nonparametric Micro Approach Reflecting the Natural Uncertainty of Statistical Matching with Categorical Data

We develop the first statistical matching micro approach reflecting the natural uncer- tainty arising during the integration of categorical data. A complete synthetic file is obtained by imprecise imputation, replacing missing entries by sets of suitable values. We discuss three imprecise imputation strategies and raise ideas on potential refine- ments by logical constraints or likelihood-based arguments. Additionally, we show how imprecise imputation can be embedded into the theory of finite random sets, providing tight lower and upper bounds for parameters. Our simulation results corroborate that their narrowness is practically relevant and that they almost always cover the true parameters