Identification in parametric models : the minimum Hellinger distance criterion

This note studies the criterion for identifiability in parametric models based on the minimization of the Hellinger distance and exhibits its relationship to the identifiability criterion based on the Fisher matrix. It shows that the Hellinger distance criterion serves to establish identifiability of parameters of interest, or lack of it, in situations where the criterion based on the Fisher matrix does not apply, like in models where the support of the observed variables depends on the parameter of interest or in models with irregular points of the Fisher matrix. Several examples illustrating this result are provided.