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Empirical φ∗-Divergence Minimizers for Hadamard Differentiable Functionals

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Topics in Nonparametric Statistics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 74))

Abstract

We study some extensions of the empirical likelihood method, when the Kullback distance is replaced by some general convex divergence or φ-discrepancy. We show that this generalized empirical likelihood method is asymptotically valid for general Hadamard differentiable functionals.

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Notes

  1. 1.

    This research was partially developed within the MME-DII Center of Excellence (ANR-11-LABX-0023-01).

  2. 2.

    ∗The first author acknowledges the support of the French Agence Nationale de la Recherche (ANR) under grant ANR-13-BS-01-0005 (project SPADRO).

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Author information

Authors and Affiliations

  1. MODAL’X, University Paris-Ouest, Nanterre, France

    Patrice Bertail

  2. CREST-LS, Malakoff, France

    Patrice Bertail & Emmanuelle Gautherat

  3. REGARDS, University of Reims, Reims, France

    Emmanuelle Gautherat

  4. ENS-Cachan, Cachan, France

    Hugo Harari-Kermadec

Authors
  1. Patrice Bertail
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  2. Emmanuelle Gautherat
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  3. Hugo Harari-Kermadec
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Corresponding author

Correspondence to Patrice Bertail .

Editor information

Editors and Affiliations

  1. Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania, USA

    Michael G. Akritas

  2. Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA

    S. N. Lahiri

  3. Department of Mathematics, University of California, San Diego, California, USA

    Dimitris N. Politis

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Bertail, P., Gautherat, E., Harari-Kermadec, H. (2014). Empirical φ∗-Divergence Minimizers for Hadamard Differentiable Functionals. In: Akritas, M., Lahiri, S., Politis, D. (eds) Topics in Nonparametric Statistics. Springer Proceedings in Mathematics & Statistics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0569-0_3

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