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Maximum d’entropie et problème des moments: Cas multidimensionnel. (Maximum entropy and the moment problem: Multidimensional case). (French) Zbl 0766.60003
Summary: We study the maximum entropy method on the mean developed by D. Dacunha-Castelle and the first author [Ann. Inst. H. Poincaré, Probab. Stat. 26, No. 4, 567-596 (1990; Zbl 0788.62007)] to reconstruct a density under linear and non-linear convex constraints. We extend the procedure to the case of a locally convex topological linear space under large deviation assumptions. We give various applications: the most important gives a solution to the generalized moment problem on a polytope.

MSC:
60A99 Foundations of probability theory
62B10 Statistical aspects of information-theoretic topics
62A01 Foundations and philosophical topics in statistics
44A60 Moment problems
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