This article considers estimating the smoothness parameter of a class of nonstationary Gaussian random fields on using irregularly spaced data observed along a curve. The set of covariance functions includes a nonstationary version of the Matérn covariance function as well as isotropic Matérn covariance function. Smoothness estimators are constructed via higher-order quadratic variations. Under mild conditions, these estimators are shown to be strongly consistent and convergence rate upper bounds are established with respect to fixed-domain asymptotics. Simulations indicate that the proposed estimators perform well for moderate sample sizes.
The authors were supported in part by AcRF Tier 1 Grant R-155-000-209-114.
We would like to thank Professor Domenico Marinucci, an Associate Editor and two referees for their comments and suggestions that led to numerous improvements to this article.
"Smoothness estimation of nonstationary Gaussian random fields from irregularly spaced data observed along a curve." Electron. J. Statist. 15 (2) 6071 - 6150, 2021. https://doi.org/10.1214/21-EJS1941