Journal
JOURNAL OF MULTIVARIATE ANALYSIS
Volume 150, Issue -, Pages 245-266Publisher
ELSEVIER INC
DOI: 10.1016/j.jmva.2016.06.003
Keywords
Inversion-free estimation; Covariance function; Stationary Gaussian process; Asymptotic analysis
Categories
Funding
- NSF [ACI-1047871, 1422157, 1217880, 0953135, DMS-1351362, NSF CNS-1409303, NSF CCF-1115769]
- Direct For Mathematical & Physical Scien [1351362] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1351362] Funding Source: National Science Foundation
- Office of Advanced Cyberinfrastructure (OAC)
- Direct For Computer & Info Scie & Enginr [1342076] Funding Source: National Science Foundation
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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. (C) 2016 Elsevier Inc. All rights reserved.
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