  We study the problem of constructing honest and adaptive confidence intervals
for the tail coefficient in the second order Pareto model, when the second
order coefficient is unknown. This problem is translated into a testing problem
on the second order parameter. By constructing an appropriate model and an
associated test statistic, we provide a uniform and adaptive confidence
interval for the first order parameter. We also provide an almost matching
lower bound, which proves that the result is minimax optimal up to a
logarithmic factor.
