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October 2005 Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields
Wei-Liem Loh
Ann. Statist. 33(5): 2344-2394 (October 2005). DOI: 10.1214/009053605000000516

Abstract

Stein [Statist. Sci. 4 (1989) 432–433] proposed the Matérn-type Gaussian random fields as a very flexible class of models for computer experiments. This article considers a subclass of these models that are exactly once mean square differentiable. In particular, the likelihood function is determined in closed form, and under mild conditions the sieve maximum likelihood estimators for the parameters of the covariance function are shown to be weakly consistent with respect to fixed-domain asymptotics.

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Wei-Liem Loh. "Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields." Ann. Statist. 33 (5) 2344 - 2394, October 2005. https://doi.org/10.1214/009053605000000516

Information

Published: October 2005
First available in Project Euclid: 25 November 2005

zbMATH: 1086.62111
MathSciNet: MR2211089
Digital Object Identifier: 10.1214/009053605000000516

Subjects:
Primary: 62D05
Secondary: 62E20 , 62G15

Keywords: computer experiment , consistency , fixed-domain asymptotics , Gaussian random field , Matérn-type covariance function , sieve maximum likelihood estimation

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 5 • October 2005
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