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Invariance of decision functions under lie groups I

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Part of the Lecture Notes in Mathematics book series (LNM,volume 296)

Keywords

  • Decision Problem
  • Decision Function
  • Parameter Group
  • Infinitesimal Generator
  • Infinitesimal Transformation

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References

  1. M. Behara (1973): Statistical decision functions on metric spaces. To appear in Selecta Statistica Canadiana, vol. 3.

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  2. M. Behara and N. Giri (1971): Locally and asymptotically minimax tests of some multivariate decision problems. Archiv der Mathematik. XXII.

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  3. D.R. Brillinger (1963): Necessary and sufficient conditions for a statistical problem to be invariant under a Lie Group. Ann. Math. Statist. 34, p. 492–500.

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  4. C. Chevalley (1946): Theory of Lie Groups. Princeton University Press.

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  5. E.J. Hannan (1965): Group Representations and Applied Probability. Methuen and Co. Ltd. London.

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  6. J. Kiefer (1957): Invariance, minimax sequential estimation, and continuous time process. Ann. Math. Statist. 28, p. 573–601.

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  8. L.A. Santalo (1953): Introduction to Integral Geometry. Hermann and Cie, Paris.

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  9. M. Stone and R. von Randow (1968): Statistically inspired conditions on the group structure of invariant experiments. Zeitschrift für Wahrscheinlichkeitstheorie u. verw. Geb. 10, p. 70–80.

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© 1973 Springer-Verlag

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Behara, M. (1973). Invariance of decision functions under lie groups I. In: Behara, M., Krickeberg, K., Wolfowitz, J. (eds) Probability and Information Theory II. Lecture Notes in Mathematics, vol 296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059826

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  • DOI: https://doi.org/10.1007/BFb0059826

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06211-0

  • Online ISBN: 978-3-540-38485-4

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