  Let $X_1, \ldots, X_n$ be some i.i.d. observations from a heavy tailed
distribution $F$, i.e. such that the common distribution of the excesses over a
high threshold $u_n$ can be approximated by a Generalized Pareto Distribution
$G_{\gamma,\sigma_n}$ with $\gamma >0$. This work is devoted to the problem of
finding confidence regions for the couple $(\gamma,\sigma_n)$ : combining the
empirical likelihood methodology with estimation equations (close but not
identical to the likelihood equations) introduced by J. Zhang (Australian and
New Zealand J. Stat n.49(1), 2007), asymptotically valid confidence regions for
$(\gamma,\sigma_n)$ are obtained and proved to perform better than Wald-type
confidence regions (especially those derived from the asymptotic normality of
the maximum likelihood estimators). By profiling out the scale parameter,
confidence intervals for the tail index are also derived.
