Uncertainty in statistical matching for discrete categorical variables

Statistical matching has the objective to estimate a joint distribution of two r.v. (Y;Z) when two sample surveys on (X;Y) and (X;Z) are available, X being a set of common variables in the two surveys. The aim of this paper is to analyze the uncertainty (due to the lack of joint sample information on (Y;Z)) in statistical matching for ordered categorical variables. The notion of uncertainty is first 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.