Electronic Journal of Statistics

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

Daqing Wang and Wei-Liem Loh

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 14 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1302784855

Digital Object Identifier
doi:10.1214/11-EJS607

Mathematical Reviews number (MathSciNet)
MR2792553

Zentralblatt MATH identifier
1274.62643

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

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

Citation

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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