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Slepian’s Inequality, Modularity and Integral Orderings

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High Dimensional Probability VI

Part of the book series: Progress in Probability ((PRPR,volume 66))

Abstract

Slepian’s inequality comes in many variants under different sets of regularity conditions. Unfortunately, some of these variants are wrong and other variants are imposing to strong regularity conditions. The first part of this paper contains a unified version of Slepian’s inequality under minimal regularity conditions, covering all the variants I know about. It is well known that Slepian’s inequality is closely connected to integral orderings in general and the supermodular ordering in particular. In the last part of the paper I explore this connection and corrects some results in the theory of integral orderings.

Mathematics Subject Classification (2010). Primary 60E15; Secondary 60A10.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aarhus, Aarhus, Denmark

    J. Hoffmann-Jørgensen

Authors
  1. J. Hoffmann-Jørgensen
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Correspondence to J. Hoffmann-Jørgensen .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, 30332, USA

    Christian Houdré

  2. University of Delaware, Newark, 19716, USA

    David M. Mason

  3. University of Tennessee, Knoxville, 37934, USA

    Jan Rosiński

  4. University of Washington, Seattle, 98195, USA

    Jon A. Wellner

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Hoffmann-Jørgensen, J. (2013). Slepian’s Inequality, Modularity and Integral Orderings. In: Houdré, C., Mason, D., Rosiński, J., Wellner, J. (eds) High Dimensional Probability VI. Progress in Probability, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0490-5_2

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