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

机译:经验披披差异和拟经验似然:指数界

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摘要

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.
机译:当Kullback距离被一些一般的凸散度代替时,我们回顾了所谓的广义经验似然法的一些最新扩展。我们建议使用一些正则化形式或准经验似然方法来代替经验似然法,该方法对应于Kullback和χ2差异的凸组合。我们表明,对于此组合中的权重的一些适当选择,相应的准经验似然是Bartlett可校正的。我们还为使用此方法获得的置信区域建立了一些非渐近的指数界。这些界限是通过作者在先前工作中获得的多元情况下自归一化和的界限得出的。我们还表明,这种结果可以扩展到过程值无限维参数。在这种情况下,一些有关自规范化过程的已知结果可用于控制广义经验似然的行为。

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