Interpolation of Spatial Data: Some Theory for KrigingPrediction of a random field based on observations of the random field at some set of locations arises in mining, hydrology, atmospheric sciences, and geography. Kriging, a prediction scheme defined as any prediction scheme that minimizes mean squared prediction error among some class of predictors under a particular model for the field, is commonly used in all these areas of prediction. This book summarizes past work and describes new approaches to thinking about kriging. |
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asymptotically optimal autocovariance function based on observing BLUP consider convergence corresponding covariance function covariance structure Cressie defined distribution E₁e EBLUPS empirical semivariogram Eoeo equivalence evenly spaced example Exercise extrapolation field on Rd Figure finite Fisher information matrix fixed-domain asymptotics fo(w Gaussian measures Gaussian model Gaussian process Gaussian random field high frequency behavior Hilbert space implies inner product integrable interpolation isotropic isotropic autocovariance function K₁ K₁(t Ko(t kriging likelihood function linear predictors Matérn model maximum likelihood mean function mean square differentiable measurement error microergodic misspecifying orthogonal P₁ Plausible Approximation plug-in predictors predictand predicting Z(0 prediction error principal irregular term problem proof pseudo-BLPs random variables REML estimate second-order structure Section sequence simulation spatial spectral density stationary process Statist Stein Suppose Theorem unknown parameters values variance Z(xo