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