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Abstract:
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Although the parameters in a finite mixture model are unidentifiable, there is a form of local identifiability guaranteeing the existence of the identifiable parameter regions. To verify its existence, practitioners use the Fisher information on the estimated parameters. However, there exist model/data situations where local identifiability based on Fisher information does not correspond to that based on the likelihood. In this talk, we propose a method to empirically measure degree of local identifiability on the estimated parameters, empirical identifiability, based on the topology of the likelihood and one's ability to construct an identifiable likelihood set. We will argue that for a likelihoodist, the proposed method is the gold standard solution to this problem.
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