Gaussian random fields are commonly used as models for spatial processes and maximum likelihood is a preferred method of choice for estimating the covariance parameters. However if the sample size n is large, evaluating the likelihood can be a numerical challenge. Covariance tapering is a way of approximating the covariance function with a taper (usually a compactly supported function) so that the computational burden is reduced. This article studies the fixed-domain asymptotic behavior of the tapered MLE for the microergodic parameter of a Matérn covariance function when the taper support is allowed to shrink as n→∞. In particular if the dimension of the underlying space is ≤3, conditions are established in which the tapered MLE is strongly consistent and also asymptotically normal. Numerical experiments are reported that gauge the quality of these approximations for finite n.
"On fixed-domain asymptotics and covariance tapering in Gaussian random field models." Electron. J. Statist. 5 238 - 269, 2011. https://doi.org/10.1214/11-EJS607