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Iterated Jackknives and Two-Sided Variance Inequalities

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High Dimensional Probability VIII

Part of the book series: Progress in Probability ((PRPR,volume 74))

Abstract

We consider the variance of a function of n independent random variables and provide inequalities that generalize previous results obtained for i.i.d. random variables. In particular we obtain upper and lower bounds on the variance based on iterated jackknife statistics that can be considered generalizations of the Efron–Stein inequality.

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Acknowledgements

C. Houdré was partially supported by the grant # 524678 from the Simons Foundation and by a Simons Fellowship grant # 267336. This material is also based in part upon material supposed by NSF grant No. 1440140 while this author was in residence at MSRI in Berkeley, CA, during Fall, 2017.

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Authors and Affiliations

  1. Google Research, Brain Team, Zürich, Switzerland

    Olivier Bousquet

  2. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA

    Christian Houdré

Authors
  1. Olivier Bousquet
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  2. Christian Houdré
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Corresponding author

Correspondence to Christian Houdré .

Editor information

Editors and Affiliations

  1. MAP 5, Université Paris Descartes, Paris, France

    Nathael Gozlan

  2. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Rafał Latała

  3. Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau, France

    Karim Lounici

  4. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA

    Mokshay Madiman

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Bousquet, O., Houdré, C. (2019). Iterated Jackknives and Two-Sided Variance Inequalities. In: Gozlan, N., Latała, R., Lounici, K., Madiman, M. (eds) High Dimensional Probability VIII. Progress in Probability, vol 74. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-26391-1_4

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