The Annals of Statistics

Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields

Wei-Liem Loh

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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.

Article information

Ann. Statist., Volume 33, Number 5 (2005), 2344-2394.

First available in Project Euclid: 25 November 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62D05: Sampling theory, sample surveys
Secondary: 62E20: Asymptotic distribution theory 62G15: Tolerance and confidence regions

Computer experiment consistency fixed-domain asymptotics Gaussian random field Matérn-type covariance function sieve maximum likelihood estimation


Loh, Wei-Liem. Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields. Ann. Statist. 33 (2005), no. 5, 2344--2394. doi:10.1214/009053605000000516.

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