Electronic Journal of Statistics

On fixed-domain asymptotics and covariance tapering in Gaussian random field models

Daqing Wang and Wei-Liem Loh

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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.

Article information

Electron. J. Statist., Volume 5 (2011), 238-269.

First available in Project Euclid: 14 April 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M30: Spatial processes
Secondary: 62E20: Asymptotic distribution theory 62G15: Tolerance and confidence regions

Asymptotic normality covariance tapering fixed-domain asymptotics Gaussian random field Matérn covariance maximum likelihood estimation spatial statistics strong consistency


Wang, Daqing; Loh, Wei-Liem. On fixed-domain asymptotics and covariance tapering in Gaussian random field models. Electron. J. Statist. 5 (2011), 238--269. doi:10.1214/11-EJS607. https://projecteuclid.org/euclid.ejs/1302784855

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