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Extension of the variance function of a steep exponential family

Le : 15/01/2007 11h45
Par : A. Masmoudi (Université de Sfax, Tunisie)
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Résumé : Let F be a multidimensional steep natural exponential family parameterized by its domain of the means MF and let VF be its variance function. This paper studies the boudary behaviour of VF : Necessary and sufficient conditions on a point m of the boundary of MF are given so that VF admits a continuous extension VF at the point m. It is also shown that the existence of VF implies the existence of a limit distribution P(m) concentrated on an exposed face of MF containing m: The relation between VF and P(m) is established and some illustrating examples are given.