The primary objective of this study is to propose an estimator of the parameters of the generalized Gaussian noise model with desirable asymptotic properties, namely, asymptotic consistency and asymptotic efficiency. Three estimators are proposed and analyzed. The relative merits and demerits of these estimators are pointed out through an analysis of their asymptotic variances and the computational complexity involved in each estimation procedure. It will be established that while the moment-method is computationally expedient, the maximum likelihood estimator is asymptotically efficient. In addition, the asymptotic relative efficiency of the moment-method with respect to the efficient likelihood estimator is found to be high in the region of the parameter space of practical interest. The maximum likelihood estimation procedure, on the other hand, is found to be computationally cumbersome. The use of the moment-method estimator as a first approximation leads to a computationally expedient and asymptotically consistent and efficient moment/Newton-step estimator.