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Sufficiency and Jensen's inequality for conditional expectations

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Abstract

For finite sets of probability measures, sufficiency is characterized by means of certain positively homogeneous convex functions. The essential tool is a discussion of equality in Jensen's inequality for conditional expectations. In particular, it is shown that characterizations of sufficiency by Csiszár's f-divergence (1963, Publ. Math. Inst. Hung. Acad. Sci. Ser. A, 8, 85–107) and by optimal solutions of a Bayesian decision problem used by Morse and Sacksteder (1966, Ann. Math. Statist., 37, 203–214) can be proved by the same method.

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Authors and Affiliations

  1. Institut für Mathematische Statistik der Universität Münster, Einsteinstraße 62, D-4400, Münster, West Germany

    Dieter Mussmann

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  1. Dieter Mussmann
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Mussmann, D. Sufficiency and Jensen's inequality for conditional expectations. Ann Inst Stat Math 40, 715–726 (1988). https://doi.org/10.1007/BF00049428

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  • DOI: https://doi.org/10.1007/BF00049428

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