Uncertainty analysis for statistical matching of ordered categorical variables

The aim is to analyze the uncertainty in statistical matching for ordered categorical variables. Uncertainty in statistical matching consists in estimating a joint distribution by observing only samples from its marginals. Unless very restrictive conditions are met, observed data do not identify the joint distribution to be estimated, and this is the reason of uncertainty. The notion of uncertainty is first formally introduced, and a measure of uncertainty is then proposed. Moreover, the reduction of uncertainty in the statistical model due to the introduction of logical constraints is investigated and evaluated via simulation.