Abstract
A method is proposed for estimating the microergodic parameters (including the smoothness parameter) of stationary Gaussian random fields on with isotropic Matérn covariance functions using irregularly spaced data. This approach uses higher-order quadratic variations and is applied to three designs, namely stratified sampling design, randomized sampling design and deformed lattice design. Microergodic parameter estimators are constructed for each of the designs. Under mild conditions, these estimators are shown to be consistent with respect to fixed-domain asymptotics. Upper bounds to the convergence rate of the estimators are also established. A simulation study is conducted to gauge the accuracy of the proposed estimators.
Funding Statement
The first author was supported by AcRF Tier 1 Grant R-155-000-209-114.
Dedication
Dedicated to Louis H. Y. Chen on his eightieth birthday
Acknowledgments
We would like to thank Professor Ming Yuan, an Associate Editor and a referee for their comments and suggestions that led to numerous improvements to this article.
Funding Statement
The first author was supported by AcRF Tier 1 Grant R-155-000-209-114.
Dedication
Dedicated to Louis H. Y. Chen on his eightieth birthday
Acknowledgments
We would like to thank Professor Ming Yuan, an Associate Editor and a referee for their comments and suggestions that led to numerous improvements to this article.
Citation
Wei-Liem Loh. Saifei Sun. Jun Wen. "On fixed-domain asymptotics, parameter estimation and isotropic Gaussian random fields with Matérn covariance functions." Ann. Statist. 49 (6) 3127 - 3152, December 2021. https://doi.org/10.1214/21-AOS2077
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