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Stability of Cramer’s Characterization of Normal Laws in Information Distances

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Book cover High Dimensional Probability VII

Part of the book series: Progress in Probability ((PRPR,volume 71))

Abstract

Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer’s theorem with respect to relative entropy and Fisher information distance.

Mathematics Subject Classification (2010). Primary 60E

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Acknowledgements

The authors are grateful to the referee for careful reading of the paper and valuable remarks. Bobkov’s research was partially supported by SFB 701 at Bielefeld University, Humboldt Foundation and NSF grant DMS-1612961. Chystyakov and Götze’s research was partially supported by SFB 701.

Author information

Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN, 55455, USA

    Sergey Bobkov

  2. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    Gennadiy Chistyakov & Friedrich Götze

Authors
  1. Sergey Bobkov
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  2. Gennadiy Chistyakov
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  3. Friedrich Götze
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Corresponding author

Correspondence to Friedrich Götze .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, Georgia, USA

    Christian Houdré

  2. University of Delaware, Department of Applied Economics and Stat University of Delaware, Newark, Delaware, USA

    David M. Mason

  3. Centre national de la recherche scientifique, Laboratoire J.A. Dieudonné, Université Côte d’Azur, Nice, France

    Patricia Reynaud-Bouret

  4. Department of Mathematics, University of Tennessee Department of Mathematics, Knoxville, Tennessee, USA

    Jan Rosiński

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Bobkov, S., Chistyakov, G., Götze, F. (2016). Stability of Cramer’s Characterization of Normal Laws in Information Distances. In: Houdré, C., Mason, D., Reynaud-Bouret, P., Rosiński, J. (eds) High Dimensional Probability VII. Progress in Probability, vol 71. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-40519-3_1

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