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2019 Local inversion-free estimation of spatial Gaussian processes
Hossein Keshavarz, XuanLong Nguyen, Clayton Scott
Electron. J. Statist. 13(2): 4224-4279 (2019). DOI: 10.1214/19-EJS1592


Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for large number of (possibly) irregularly spaced observations, due to the need to handle the inverse of ill-conditioned and large covariance matrices. Extending the “inversion-free” method of Anitescu, Chen and Stein [1], we investigate a broad class of covariance parameter estimation based on inversion-free surrogate losses and block diagonal approximation schemes of the covariance structure. This class of estimators yields a spectrum for negotiating the trade-off between statistical accuracy and computational cost. We present fixed-domain asymptotic properties of our proposed method, establishing $\sqrt{n}$-consistency and asymptotic normality results for isotropic Matern Gaussian processes observed on a multi-dimensional and irregular lattice. Simulation studies are also presented for assessing the scalability and statistical efficiency of the proposed algorithm for large data sets.


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Hossein Keshavarz. XuanLong Nguyen. Clayton Scott. "Local inversion-free estimation of spatial Gaussian processes." Electron. J. Statist. 13 (2) 4224 - 4279, 2019.


Received: 1 November 2018; Published: 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07136616
MathSciNet: MR4021265
Digital Object Identifier: 10.1214/19-EJS1592

Primary: 62M30 , 62M40
Secondary: 60G15

Keywords: computationally scalable , fixed-domain asymptotic analysis , Gaussian process , irregularly spaced observations , Local inversion-free covariance estimation


Vol.13 • No. 2 • 2019
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