  Using multiple stochastic integrals and the Malliavin calculus, we analyze
the asymptotic behavior of quadratic variations for a specific non-Gaussian
self-similar process, the Rosenblatt process. We apply our results to the
design of strongly consistent statistical estimators for the self-similarity
parameter $H$. Although, in the case of the Rosenblatt process, our estimator
has non-Gaussian asymptotics for all $H>1/2$, we show the remarkable fact that
the process's data at time 1 can be used to construct a distinct, compensated
estimator with Gaussian asymptotics for $H\in(1/2,2/3)$.
