Least squares estimation of nonlinear spatial trends

The goal of this work is to study the asymptotic and finite sample properties of an estimator of a nonlinear regression function when errors are spatially correlated, and when the spatial dependence structure is unknown. The proposed method is based on a weighted nonlinear least squares approach, taking into account the spatial covariance. Weak consistency of the regression parameters estimator is derived, along with its asymptotic Gaussian limit. The behavior of the proposed estimator is illustrated with a simulation study, considering different correlation structures in R2 and a more general case including a spatial covariate. The method is also applied to two real data cases.