Proofs for empirical likelihood with general f -divergences

We study extensions of empirical likelihood where the log likelihood ratio is replaced withgeneral f -divergences (which we call empirical divergences). First, we give a novel, elementaryproof forχd-calibration that does not use duality. We then see how to rigorously prove coveragerates for empirical divergence confidence regions by going beyond the asymptotic expansion forthe profile likelihood. Finally, we extend the high dimensional theory for empirical likelihoodto general f -divergences and show that the Euclidean divergence gives stronger guarantees inhigh dimensional settings.