The Annals of Statistics

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

Wei-Liem Loh

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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.

Article information

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

Dates
First available in Project Euclid: 25 November 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1132936566

Digital Object Identifier
doi:10.1214/009053605000000516

Mathematical Reviews number (MathSciNet)
MR2211089

Zentralblatt MATH identifier
1086.62111

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1132936566


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