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Optical local Gaussian approximation of an exponential family
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  • Published: September 1987

Optical local Gaussian approximation of an exponential family

  • Enno Mammen1 

Probability Theory and Related Fields volume 76, pages 103–119 (1987)Cite this article

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Summary

Under certain regularity conditions products E n of an experiment E can be locally approximated by homoschedastic Gaussian experiments G n. G n can be defined such that the square roots of the densities have nearly the same structure with respect to the L 2-geometry as in E n. The main result of this paper is that this choice of G n is asymptotically optimal in the sense of minimizing the deficiency distance between E n and G if E is a one-dimensional exponential family.

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Author information

Authors and Affiliations

  1. Sonderforschungsbereich 123, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900, Heidelberg, Federal Republic of Germany

    Enno Mammen

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  1. Enno Mammen
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Additional information

This work has been supported by the Deutsche Forschungsgemeinschaft

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Cite this article

Mammen, E. Optical local Gaussian approximation of an exponential family. Probab. Th. Rel. Fields 76, 103–119 (1987). https://doi.org/10.1007/BF00390278

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  • Received: 01 January 1985

  • Revised: 10 April 1987

  • Issue Date: September 1987

  • DOI: https://doi.org/10.1007/BF00390278

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Condition Product
  • Regularity Condition
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