Behavior of L1-based probabilistic correction applied to statistical matching with misclassification information

We illustrate the use of a recently proposed efficient procedure, based on L1 distance minimization, for correcting inconsistent (i.e. incoherent) probability assessments for the so named statistical matching problem. Albeit the statistical matching problem is based on conditional probabilities estimates, inconsistencies can appear only among assessments given on the same conditioning values, hence a correction instance can be splitted in a finite set of unconditional correction instances where the L1-based correction can efficiently operate. The statistical matching problem has been recently enriched with the possibility of a misclassification setting, breaking the aforementioned segmentation possibility. Anyhow the L1-based procedure can be applied by a straightforward translation in a MIP problem, albeit the set of consistent solutions turns out to be not convex and hence potential disconnected solutions can appear.