The whittle estimator for strongly dependent stationary Gaussian fields

In this article we generalize results on the asymptotic behaviour of the Wh ittle estimator for certain stationary Gaussian long range dependent fields . These results ha have been established in the one-dimensional case under very general conditions. They require controlling the estimation bias and a lso giving convergence theorems for certain quadratic forms of the observat ions. In the multidimensional setting, our main interest,will be controllin g the bias. This can be done for d less than or equal to 3 using taper func tions, and, depending on the shape of the singularity, also introducing cer tain regularizing functions. In this last case, however, the estimator will no longer be efficient. We also present certain partial results concerning the convergence to a limiting Gaussian distribution of the associated quad ratic forms.