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Invariant finite-dimensional exponential families on homogeneous spaces

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Abstract

A general form is obtained for the finite-dimensional exponential family invariant with respect to a locally compact group G when it is defined on the measurable quotient spade (G/Γ,A,μ) of this group with respect to a subgroup Γ. Conditions for the existence of such families are derived. Examples are given of exponential families on a compact homogeneous space, and the general form of families in Rn invariant with respect to GL(n) is obtained.

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Literature cited

  1. L. S. Pontryagin, Continuous Groups [in Russian], Moscow (1954).

  2. I. M. Gel'fand and M. I. Graev, “Finite-dimensional irreducible representations of unitary and complete linear groups and related special functions,” Izv. Akad. Nauk SSSR, Ser. Matem.,29, 1329–1356 (1965).

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  3. V. M. Maksimov, “Necessary and sufficient statistics for a family of probability distributions on bicompact topological groups,” Teor. Veroyatnost. i Primenen.,12, No. 2, 307–321 (1967).

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Authors and Affiliations

  1. A. M. Gor'ki Perm State University, USSR

    P. N. Sapozhnikov

Authors
  1. P. N. Sapozhnikov
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Additional information

Translated from Matematicheskie Zametki, Vol. 7, No. 6, pp. 707–715, June, 1970.

The author wishes to thank V. N. Tutubalin for his great interest in this work.

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Sapozhnikov, P.N. Invariant finite-dimensional exponential families on homogeneous spaces. Mathematical Notes of the Academy of Sciences of the USSR 7, 427–431 (1970). https://doi.org/10.1007/BF01093600

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  • DOI: https://doi.org/10.1007/BF01093600

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