Least squares estimation of nonlinear spatial trends

Crujeiras, Rosa M.;Van Keilegom, Ingrid
(2010) Computational Statistics & Data Analysis — Vol. 54, n° 2, p. 452-465 (2010)

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Abstract
Results on 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 are derived. The proposed method is based on a generalized 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 R-2 and a more general case including a spatial covariate. The method is also applied to two real data cases. (C) 2009 Elsevier B.V. All rights reserved.
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Crujeiras, R. M., & Van Keilegom, I. (2010). Least squares estimation of nonlinear spatial trends. Computational Statistics & Data Analysis, 54(2), 452-465. https://doi.org/10.1016/j.csda.2009.09.014 (Original work published 2010)