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This paper presents two results concerning uniform confidence intervals forthe tail index and the extreme quantile. First, we show that it is impossibleto construct a length-optimal confidence interval satisfying the correctuniform coverage over a local non-parametric family of tail distributions.Second, in light of the impossibility result, we construct honest confidenceintervals that are uniformly valid by incorporating the worst-case bias in thelocal non-parametric family. The proposed method is applied to simulated dataand a real data set of National Vital Statistics from National Center forHealth Statistics.

On Uniform Confidence Intervals for the Tail Index and the Extreme Quantile