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Article Dans Une Revue ESAIM: Proceedings and Surveys Année : 2015

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

Résumé

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 χ2 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.

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Dates et versions

hal-01376331 , version 1 (04-10-2016)

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Hugo Harari-Kermadec, Emmanuelle Gautherat, Patrice Bertail. Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds. ESAIM: Proceedings and Surveys, 2015, 51, pp.212-231. ⟨10.1051/proc/201551012⟩. ⟨hal-01376331⟩
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