Semiparametric estimation of spatial long-range dependence

Estimation of the long-range dependence parameter in spatial processes using a semiparametric approach is studied. An extended formulation of the averaged periodogram method proposed in Robinson [1994. Semiparametric analysis of long memory time series. Ann. Statist. 22, 515-539] is derived, considering a certain homogeneous and isotropic behaviour of the spectral distribution in the low frequencies. The weak consistency of the estimator proposed is proved.