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Exact norms of a Stein-type operator and associated stochastic orderings
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  • Published: 26 August 2003

Exact norms of a Stein-type operator and associated stochastic orderings

  • Claude Lefèvre1 &
  • Sergey Utev2 

Probability Theory and Related Fields volume 127, pages 353–366 (2003)Cite this article

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  • 14 Citations

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Abstract

Motivated by asymptotic expansions in the central limit theorem, we find exact norms of a sequence of Stein-type operators. The proof is based on new stochastic comparisons in distribution between the difference of two independent transformed normal variables and the standard normal distribution.

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Author information

Authors and Affiliations

  1. Institut de Statistique et de Recherche Opérationnelle, Université Libre de Bruxelles, Boulevard du Triomphe, C.P. 210, 1050, Bruxelles, Belgique

    Claude Lefèvre

  2. School of Mathematical Sciences, University of Nottingham University Park, Nottingham, NG7 2RD, United Kingdom

    Sergey Utev

Authors
  1. Claude Lefèvre
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  2. Sergey Utev
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Corresponding author

Correspondence to Claude Lefèvre.

Additional information

Mathematics Subject Classifications (2000): 60F05; 60E15

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Cite this article

Lefèvre, C., Utev, S. Exact norms of a Stein-type operator and associated stochastic orderings. Probab. Theory Relat. Fields 127, 353–366 (2003). https://doi.org/10.1007/s00440-003-0288-9

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  • Received: 13 August 2002

  • Revised: 14 April 2003

  • Published: 26 August 2003

  • Issue Date: November 2003

  • DOI: https://doi.org/10.1007/s00440-003-0288-9

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Keywords or phrases:

  • Stein-type operator
  • Exact norms
  • Central limit theorem
  • Stochastic order in distribution
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