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Complete Probability Statistics 1 For Cambrid...

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Complete Probability Statistics 1 For Cambrid...

In this paper, we address the problem of testing hypothesesusing 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 underlyingdistribution, which is called locally conic. This method enlights howthe general model induces the structure of the limiting distributionin terms of dimensionality of some derivative space. We present variousapplications of the theory. The main application is to mixture models.Under very general assumptions, we solve completely the problem of testing the size of the mixture using maximum likelihood statistics.We derive the asymptotic distribution of the maximum likelihood statisticratio which takes an unexpected form. 781b155fdc


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