On asymptotic distribution and asymptotic efficiency of least squares estimators of spatial variogram parameters

In this article, we consider the least-squares approach for estimating parameters of a spatial variograin and establish consistency and asymptotic normality of these estimators under general conditions. Large-sample distributions are also established under a spatial regression model where the sampling design possibly has an infill sampling component. These results allow us to investigate efficiencies of different least squares variogram-parameter estimators in large samples, We provide two necessary and sufficient conditions for these estimators to be asymptotically efficient, It is an interesting consequence of our results that when the number of lags used to define the estimators is chosen to be equal to the number of variogram parameters to be estimated, the ordinary least squares estimator, the weighted least squares and the generalized least squares estimators are all asymptotically efficient. (C) 2002 Elsevier Science B.V. All rights reserved.