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Analyses factorielles des distributions marginales de processus

Abstract : We define an affinity measure of two probability density functions of p-dimensionnal random vectors by their inner product in the space of the square integrable functions. We compute it for different types of densities. We present the asymptotic properties of this measure in the Gaussian case and we prove in particular its asymptotic normality when the parameters are estimated by the maximum likelihood method. We use this measure to define principal components analysis of T densities (or characteristic functions) the aim being to evaluate their evolution by visualizing them in low dimensionnal spaces. We study its relations with Dual Statis method on variance matrices and we propose a convergent estimation. We show representations obtained on cardiology data and process data with variations on their parameters. To these densities indexed by t (t=1,...,T) we add a nominal variable Y on the indexes. This variable generates a density partition into Q categories. We define a discriminant analysis and suggest four rules to assign a new density to one of these Q categories. Two rules are probabilistic, based on the asymptotic normality of the affinity measure; the two others are geometrical, based on the distance derived from the affinity measure. We illustrate this method with archeological data (measures on Alsace castles stones). As an application, a dating method for the castles is proposed.
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Submitted on : Wednesday, February 18, 2004 - 10:15:42 AM
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  • HAL Id : tel-00004806, version 1

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Rachid Boumaza. Analyses factorielles des distributions marginales de processus. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1999. Français. ⟨tel-00004806⟩

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