Probability envelopes and their Dempster-Shafer approximations 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 integration of data sets where some variables are separately observed and some others are observed in all the data sets. This problem leads to the issue of non-uniqueness for the compatible (conditional) distributions and so it suggests to deal with sets of probabilities. For that we consider different strategies to get a (conditional) belief function that approximates the lower envelope of the class of compatible (conditional) probabilities. We first analyze the case without logical constraints among the variables and then generalize the obtained results by allowing for logical constraints. We finally show an application to real data.