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

Patrice Bertail, Emmanuelle Gautherat and Hugo Harari-Kermadec
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Patrice Bertail: Crest
Emmanuelle Gautherat: Crest
Hugo Harari-Kermadec: Crest

No 2005-34, Working Papers from Center for Research in Economics and Statistics

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.

Pages: 37
Date: 2005
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