  We consider a modified quadratic variation of the Hermite process based on
some well-chosen increments of this process. These special increments have the
very useful property to be independent and identically distributed up to
asymptotically negligible remainders. We prove that this modified quadratic
variation satisfies a Central Limit Theorem and we derive its rate of
convergence under the Wasserstein distance via Stein-Malliavin calculus. As a
consequence, we construct, for the first time in the literature related to
Hermite processes, a strongly consistent and asymptotically normal estimator
for the Hurst parameter.
