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Testing in locally conic models, and application to mixture models

Didier Dacunha-CastelleElisabeth Gassiat — 2010

ESAIM: Probability and Statistics

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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