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

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

2006-02-14

arxiv.org/abs/math/0602302v1

Annals of Statistics 2005, Vol. 33, No. 5, 2344-2394

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000516 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000516

Stein [Statist. Sci. 4 (1989) 432--433] proposed the Mat\'{e}rn-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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