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Extrema de processus stochastiques. Propriétés asymptotiques de tests d'hypothèses

Abstract : The following thesis falls into two parts.
The first part is concerned with the extreme value theory. This domain intends to compute the probability of rare events. The first work gives the asymptotic order of the maximum of a non-stationary Gaussian process with constant variance. The second work characterizes the law of the maximum in finite time and consequently for all sorts of levels. Moreover, the estimating procedure led to the creation of a Matlab toolbox called MAGP.
The second part contains two statistical applications. On the one hand, the distribution and power of the likelihood ratio test statistics are studied for finite mixture models. On the other hand, the construction of a test of sphericity is analyzed with extreme eigenvalues of covariance matrices.
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Contributor : Cécile Mercadier <>
Submitted on : Thursday, September 8, 2005 - 1:59:42 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:33:18 PM


  • HAL Id : tel-00010070, version 1


Cécile Mercadier. Extrema de processus stochastiques. Propriétés asymptotiques de tests d'hypothèses. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2005. Français. ⟨tel-00010070⟩



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