On Ambiguity Arising from Partially Identified Models

While the existence of the intrinsic ambiguity arising from partially identified statistical models have actually led statisticians and econometricians to focus on (identified) sets estimation using random set statistics, the issue of decision-making under ambiguity with such models seems lacking. Perhaps this is due to the fact that general uncertainty analysis is not quite familiar to statisticians. As such, this paper aims at calling the attention of statisticians and econometricians to a variety of methodologies, in the literature, which provide non-additive uncertainty measures for ambiguous events which could be useful for statistical analysis of partially identified models, such as imprecise probabilities, possibility and idempotent probability theories, belief functions, Choquet capacities and fuzzy measures.