Abstract
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.
Highlights
IntroductionThe main result in this note is to show that the Hellinger distance criterion can be used to verify the (local) identifiability of a parameter of interest, or lack of it, either in models or points in the parameter space where the Fisher matrix criterion does not apply
The main result in this note is to show that the Hellinger distance criterion can be used to verify the identifiability of a parameter of interest, or lack of it, either in models or points in the parameter space where the Fisher matrix criterion does not apply
The following examples illustrate the use of Proposition 1 and the definitions introduced so far. They are going to illustrate, the regularity conditions employed by Rothenberg (1971) to obtain a criterion for local identifiability based on the Fisher matrix
Summary
The main result in this note is to show that the Hellinger distance criterion can be used to verify the (local) identifiability of a parameter of interest, or lack of it, either in models or points in the parameter space where the Fisher matrix criterion does not apply This note illustrates this result with several examples, including a parametric procurement auction model, the uniform, normal squared, and Laplace location models.
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