Semiparametric nonlinear log-periodogram regression estimation for perturbed stationary anisotropic long memory random fields

In recent years, spatial statistics has been widely used in many fields. The applications of two-dimensional random fields to describe data in image processing, environment and earth science, space econometrics and other fields are ubiquitous. Considering the complexity of two-dimensional spatial data, two kinds of semiparametric nonlinear log-periodogram regression (NLPR) estimations are proposed to estimate memory parameters d=(d(1),d(2))' of perturbed two-dimensional anisotropic stationary long memory random fields. The long memory parameters d(1) in the "vertical" and d(2) in the "horizontal" direction respectively, and 0<d(1),d(2)<0.5. The anisotropic stationary long memory random field is disturbed by an independent, additive, and stationary Gaussian short memory noise field. The performance of the NLPR estimators is examined and compared with the performance of the GPH (Geweke and Porter-Hudak) estimators by simulation.