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In this paper, we address the problem of testing hypotheses
using maximum likelihood statistics in non identifiable models.
We derive the asymptotic distribution under very general assumptions.
The key idea is a local reparameterization, depending on the underlying
distribution, which is called locally conic. This method enlights how
the general model induces the structure of the limiting distribution
in terms of dimensionality of some derivative space. We present various
applications of...
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