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" Interpolation of Spatial Data "
by Michael L. Stein.
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BL
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| Record Number
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573548
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b402767
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| Main Entry
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Stein, Michael L.
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| Title & Author
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Interpolation of Spatial Data : Some Theory for Kriging /\ by Michael L. Stein.
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| Publication Statement
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New York, NY :: Springer New York :: Imprint: Springer,, 1999.
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| Series Statement
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Springer Series in Statistics,
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| ISBN
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9781461214946
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: 9781461271666
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| Contents
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1 Linear Prediction -- 1.1 Introduction -- 1.2 Best linear prediction -- 1.3 Hilbert spaces and prediction -- 1.4 An example of a poor BLP -- 1.5 Best linear unbiased prediction -- 1.6 Some recurring themes -- 1.7 Summary of practical suggestions -- 2 Properties of Random Fields -- 2.1 Preliminaries -- 2.2 The turning bands method -- 2.3 Elementary properties of autocovariance functions -- 2.4 Mean square continuity and differentiability -- 2.5 Spectral methods -- 2.6 Two corresponding Hilbert spaces -- 2.7 Examples of spectral densities on 112 -- 2.8 Abelian and Tauberian theorems -- 2.9 Random fields with nonintegrable spectral densities -- 2.10 Isotropic autocovariance functions -- 2.11 Tensor product autocovariances -- 3 Asymptotic Properties of Linear Predictors -- 3.1 Introduction -- 3.2 Finite sample results -- 3.3 The role of asymptotics -- 3.4 Behavior of prediction errors in the frequency domain -- 3.5 Prediction with the wrong spectral density -- 3.6 Theoretical comparison of extrapolation and ointerpolation -- 3.7 Measurement errors -- 3.8 Observations on an infinite lattice -- 4 Equivalence of Gaussian Measures and Prediction -- 4.1 Introduction -- 4.2 Equivalence and orthogonality of Gaussian measures -- 4.3 Applications of equivalence of Gaussian measures to linear prediction -- 4.4 Jeffreys's law -- 5 Integration of Random Fields -- 5.1 Introduction -- 5.2 Asymptotic properties of simple average -- 5.3 Observations on an infinite lattice -- 5.4 Improving on the sample mean -- 5.5 Numerical results -- 6 Predicting With Estimated Parameters -- 6.1 Introduction -- 6.2 Microergodicity and equivalence and orthogonality of Gaussian measures -- 6.3 Is statistical inference for differentiable processes possible? -- 6.4 Likelihood Methods -- 6.5 Matérn model -- 6.6 A numerical study of the Fisher information matrix under the Matérn model -- 6.7 Maximum likelihood estimation for a periodic version of the Matérn model -- 6.8 Predicting with estimated parameters -- 6.9 An instructive example of plug-in prediction -- 6.10 Bayesian approach -- A Multivariate Normal Distributions -- B Symbols -- References.
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| Abstract
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Prediction 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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| Subject
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Statistics.
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Geography.
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Geology.
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Mathematical statistics.
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SpringerLink (Online service)
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