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

The Annals of Statistics · 2005 · Volume 33 · Issue 5

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.

Keywords

62D05, 62E20, 62G15, computer experiment, consistency, fixed-domain asymptotics, Gaussian random field, Matérn-type covariance function, sieve maximum likelihood estimation

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