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Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds

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  • Patrice Bertail

    (Crest)

  • Emmanuelle Gautherat

    (Crest)

  • Hugo Harari-Kermadec

    (Crest)

Abstract

We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and ?2 discrepancies. We show that for some adequate choice of the weight in this combination, the corresponding quasi-empirical likelihood is Bartlett-correctable. We also establish some non-asymptotic exponential bounds for the confidence regions obtained by using this method. These bounds are derived via bounds for self-normalized sums in the multivariate case obtained in a previous work by the authors. We also show that this kind of results may be extended to process valued infinite dimensional parameters. In this case some known results about self-normalized processes may be used to control the behavior of generalized empirical likelihood.

Suggested Citation

  • Patrice Bertail & Emmanuelle Gautherat & Hugo Harari-Kermadec, 2005. "Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds," Working Papers 2005-34, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2005-34
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    References listed on IDEAS

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    1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    2. Philippe Barbe & Patrice Bertail, 2004. "Testing the Global Stability of a Linear Model," Working Papers 2004-46, Center for Research in Economics and Statistics.
    3. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
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