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

By Daqing Wang, Wei-Liem Loh. 2011

60 citations recorded by the source corpus.

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.

Subfields: Earth-Surface Processes, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/cbf296d927ed1dad0226efbf71b0f8f2f0f9966e

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In Environmental Engineering

Citations in the corpus

Estimation and prediction using generalized Wendland covariance functions under fixed domain asymptotics (2016, background): “posed by Wendland (1995). Other closed form solutions of integral (1) can be obtained when κ = k + 0.”
A Case Study Competition Among Methods for Analyzing Large Spatial Data (2017, methodology): “For parameter estimation in the likelihood framework, one- and two-taper approaches exist (see Kaufman et al. 2008; Du et al. 2009; Wang and Loh 2011; Bevilacqua et al. 2016, for relevant literature).”