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

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.

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

Cited by in corpus (8)

• Fixed-domain asymptotic properties of tapered maximum likelihood estimators
• A frequency domain empirical likelihood method for irregularly spaced spatial data
• Consistent estimates of deformed isotropic Gaussian random fields on the plane
• Consistency of the mean and the principal components of spatially distributed functional data
• On the Limiting Behaviour of Needlets Polyspectra
• Gaussian semiparametric estimates on the unit sphere
• Finite-dimensional Gaussian approximation with linear inequality constraints
• Comparing Scale Parameter Estimators for Gaussian Process Interpolation with the Brownian Motion Prior: Leave-One-Out Cross Validation and Maximum Likelihood