  Gaussian random fields are a powerful tool for modeling environmental
processes. For high dimensional samples, classical approaches for estimating
the covariance parameters require highly challenging and massive computations,
such as the evaluation of the Cholesky factorization or solving linear systems.
Recently, Anitescu, Chen and Stein \cite{M.Anitescu} proposed a fast and
scalable algorithm which does not need such burdensome computations. The main
focus of this article is to study the asymptotic behavior of the algorithm of
Anitescu et al. (ACS) for regular and irregular grids in the increasing domain
setting. Consistency, minimax optimality and asymptotic normality of this
algorithm are proved under mild differentiability conditions on the covariance
function. Despite the fact that ACS's method entails a non-concave
maximization, our results hold for any stationary point of the objective
function. A numerical study is presented to evaluate the efficiency of this
algorithm for large data sets.
