
Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spaces
Optimal linear prediction (also known as kriging) of a random field {Z(x...
read it

Asymptotically Equivalent Prediction in Multivariate Geostatistics
Cokriging is the common method of spatial interpolation (best linear unb...
read it

Tangent fields, intrinsic stationarity, and selfsimilarity
This paper studies the local structure of continuous random fields on ℝ^...
read it

The Gauss Hypergeometric Covariance Kernel for Modeling SecondOrder Stationary Random Fields in Euclidean Spaces: its Compact Support, Properties and Spectral Representation
This paper presents a parametric family of compactlysupported positive ...
read it

Invariances of random fields paths, with applications in Gaussian Process Regression
We study pathwise invariances of centred random fields that can be contr...
read it

Multilevel approximation of Gaussian random fields: Covariance compression, estimation and spatial prediction
Centered Gaussian random fields (GRFs) indexed by compacta such as smoot...
read it

On the consistency of inversionfree parameter estimation for Gaussian random fields
Gaussian random fields are a powerful tool for modeling environmental pr...
read it
Equivalence of measures and asymptotically optimal linear prediction for Gaussian random fields with fractionalorder covariance operators
We consider Gaussian measures μ, μ̃ on a separable Hilbert space, with fractionalorder covariance operators A^2β resp. Ã^2β̃, and derive necessary and sufficient conditions on A, Ã and β, β̃ > 0 for I. equivalence of the measures μ and μ̃, and II. uniform asymptotic optimality of linear predictions for μ based on the misspecified measure μ̃. These results hold, e.g., for Gaussian processes on compact metric spaces. As an important special case, we consider the class of generalized WhittleMatérn Gaussian random fields, where A and Ã are elliptic secondorder differential operators, formulated on a bounded Euclidean domain 𝒟⊂ℝ^d and augmented with homogeneous Dirichlet boundary conditions. Our outcomes explain why the predictive performances of stationary and nonstationary models in spatial statistics often are comparable, and provide a crucial first step in deriving consistency results for parameter estimation of generalized WhittleMatérn fields.
READ FULL TEXT
Comments
There are no comments yet.