Journal of Official Statistics, Vol.22, No.1, 2006. pp. 137157

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Statistical Matching for Categorical Data: Displaying Uncertainty and Using Logical Constraints

Statistical matching is a technique for combining information from different sources. It can be used in situations when variables of interest are not jointly observed and conclusions must be drawn on the basis of partial knowledge of the phenomenon. Uncertainty regarding conclusions arises naturally unless strong and nontestable hypotheses are assumed. Hence, the main goal of statistical matching can be reinterpreted as the study of the key aspects of uncertainty, and what conclusions can be drawn. In this article we give a formalization of the concept of uncertainty in statistical matching when the variables are categorical, and formalize the key elements to be investigated. A consistent maximum likelihood estimator of the elements characterizing uncertainty is suggested. Furthermore, the introduction of logical constraints and their effect on uncertainty are studied. All the analyses have been performed according to the likelihood principle. An example with real data is presented and a comparison with other approaches already defined is performed.

Data fusion, synthetical matching, constrained maximum likelihood estimation, EM algorithm

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