Abstract
This article considers parameter estimation for a class of Gaussian random fields on that are observed with measurement error and irregularly spaced design sites. This class comprises Gaussian random fields with suitably smooth mean functions and isotropic powered exponential, Matérn or generalized Wendland covariance functions. Under fixed-domain asymptotics, consistent estimators are proposed for three microergodic parameters, namely the nugget, the smoothness parameter and a parameter related to the coefficient of the principal irregular term of the isotropic covariance function. Upper bounds for the convergence rate of these estimators are established. Simulations are conducted to study the finite sample accuracy of the proposed estimators.
Funding Statement
The first author was supported by AcRF Tier 1 Grant R-155-000-209-114.
Acknowledgements
The authors would like to thank Professor Davy Paindaveine, the Associate Editor and two anonymous referees for their constructive comments that improved the quality of this paper. The second author would also like to thank Professors Cheng Li, Michael Stein and Jin-Ting Zhang for their insightful comments on her PhD thesis Sun (2020).
Citation
Wei-Liem Loh. Saifei Sun. "Estimating the parameters of some common Gaussian random fields with nugget under fixed-domain asymptotics." Bernoulli 29 (3) 2519 - 2543, August 2023. https://doi.org/10.3150/22-BEJ1551
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