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 et al. (2014) 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.
Bibliographical noteFunding Information:
This research is partially supported by NSF grant ACI-1047871 . Additionally, CS is partially supported by NSF grants 1422157 , 1217880 , and 0953135 , and LN by NSF CAREER award DMS-1351362 , NSF CNS-1409303 , and NSF CCF-1115769 .
© 2016 Elsevier Inc.
- Asymptotic analysis
- Covariance function
- Inversion-free estimation
- Stationary Gaussian process