Dempster-Shafer Approximations and Probabilistic Bounds in Statistical Matching

Many economic applications require to integrate information coming from different data sources. In this work we consider a specific integration problem called statistical matching, referring to probabilistic distributions of Y|X, Z|X and X, where X, Y, Z are categorical (possibly multi-dimensional) random variables. Here, we restrict to the case of no logical relations among random variables X, Y, Z. The non-uniqueness of the conditional distribution of (Y, Z)|X suggests to deal with sets of probabilities. For that we consider different strategies to get a conditional belief function for (Y, Z)|X that approximates the initial assessment in a reasonable way. In turn, such conditional belief function, together with the marginal probability distribution of X, gives rise to a joint belief function for the distribution of V= (X, Y, Z).