
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 f...
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On a linear functional for infinitely divisible moving average random fields
Given a lowfrequency sample of the infinitely divisible moving average ...
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On Functions of Markov Random Fields
We derive two sufficient conditions for a function of a Markov random fi...
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Asymptotic analysis in multivariate average case approximation with Gaussian kernels
We consider tensor product random fields Y_d, d∈ℕ, whose covariance funt...
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Asymptotically Equivalent Prediction in Multivariate Geostatistics
Cokriging is the common method of spatial interpolation (best linear unb...
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Community detection and percolation of information in a geometric setting
We make the first steps towards generalizing the theory of stochastic bl...
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Covariance Prediction via Convex Optimization
We consider the problem of predicting the covariance of a zero mean Gaus...
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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)}_x∈X indexed by a compact metric space (X,d_X) can be obtained if the mean value function mX→R and the covariance function ϱX×X→R of Z are known. We consider the problem of predicting the value of Z(x^*) at some location x^*∈X based on observations at locations {x_j}_j=1^n which accumulate at x^* as n→∞. Our main result characterizes the asymptotic performance of linear predictors (as n increases) based on an incorrect second order structure (m̃,ϱ̃). We, for the first time, provide necessary and sufficient conditions on (m̃,ϱ̃) for asymptotic optimality of the corresponding linear predictor, without any restrictive assumptions on ϱ, ϱ̃ such as stationarity. These general results are illustrated by an example on the sphere S^2 for the case of two isotropic covariance functions.
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