Fixed-domain asymptotics for a subclass of Matérn-type Gaussian random fields. (English) Zbl 1086.62111

Summary: M. L. Stein [Stat. Sci. 4, 432–433 (1989)] 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.


62M40 Random fields; image analysis
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics


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