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Submitted by pscully on Thu, 03/04/2010 - 10:21.
03/11/2010 - 16:10
03/11/2010 - 17:30
STA/BST 290: Matthias Drton (U Chicago)
Likelihood ratio tests and singularities
Thursday, March 11th, 2010 at 4.10pm, MSB 1147 (Colloquium Room)
Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)
Speaker: Matthias Drton (U Chicago)
Title: Likelihood ratio tests and singularities
Abstract: Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theorem hold for semi-algebraic sets such that the asymptotics are determined by the tangent cone at the true parameter point. At boundary points or singularities, the tangent cone need not be a linear space and limiting distributions other than chi-square distributions may arise. While boundary points often lead to mixtures of chi-square distributions, singularities give rise to nonstandard limits. If time permits we will also briefly discuss related issues for the Bayesian information criterion.