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Title: Confidence sets for group memberships Authors:  Andreas Dzemski - University of Gothenburg (Sweden) [presenting]
Ryo Okui - NYU Shanghai (China)
Abstract: Panel models are considered where unit behavior is driven by a latent group structure. New procedures are proposed for constructing confidence sets for group memberships. We consider unitwise confidence sets as well as confidence sets for the entire group membership structure, which we call uniform confidence sets. A unitwise confidence set gives a set of possible group memberships for one specific unit and contains that units true group membership with a pre-specified probability. A uniform confidence set gives a set of possible group memberships for each unit that contains the true group memberships with a pre-specified probability. It is constructed by inverting a test that tests group memberships for all units simultaneously. Our confidence sets can be used to quantify the uncertainty about estimated group memberships. This complements previous work that focuses on inference with respect to the parameters that govern group-specific behavior. Our approach exploits the fact that the problem of sorting units into groups can be characterized by a system of moment inequalities. We construct the uniform confidence sets by stringing together unitwise confidence sets using a Bonferroni correction. The theoretical justification of this procedure exploits a high-dimensional CLT and a new anti-concentration result. We also propose an algorithm that combines moment selection with iterated hypothesis selection to eliminate units for which group membership can be precisely estimated.