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- handle: 10670/1.kh07up
- hal: hal-01376331
- doi: 10.1051/proc/201551012
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info:eu-repo/semantics/altIdentifier/doi/10.1051/proc/201551012
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Hugo Harari-Kermadec et al., « Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds », HAL-SHS : histoire, ID : 10.1051/proc/201551012
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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.