Interpolation of spatial data : some theory for kriging
著者
書誌事項
Interpolation of spatial data : some theory for kriging
(Springer series in statistics)
Springer, c1999
大学図書館所蔵 全40件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. [235]-242
Includes index
内容説明・目次
内容説明
A summary of past work and a description of new approaches to thinking about kriging, commonly used in the prediction of a random field based on observations at some set of locations in mining, hydrology, atmospheric sciences, and geography.
目次
1 Linear Prediction.- 1.1 Introduction.- 1.2 Best linear prediction.- Exercises.- 1.3 Hilbert spaces and prediction.- Exercises.- 1.4 An example of a poor BLP.- Exercises.- 1.5 Best linear unbiased prediction.- Exercises.- 1.6 Some recurring themes.- The Matern model.- BLPs and BLUPs.- Inference for differentiable random fields.- Nested models are not tenable.- 1.7 Summary of practical suggestions.- 2 Properties of Random Fields.- 2.1 Preliminaries.- Stationarity.- Isotropy.- Exercise.- 2.2 The turning bands method.- Exercise.- 2.3 Elementary properties of autocovariance functions.- Exercise.- 2.4 Mean square continuity and differentiability.- Exercises.- 2.5 Spectral methods.- Spectral representation of a random field.- Bochner's Theorem.- Exercises.- 2.6 Two corresponding Hilbert spaces.- An application to mean square differentiability.- Exercises.- 2.7 Examples of spectral densities on 112.- Rational spectral densities.- Principal irregular term.- Gaussian model.- Triangular autocovariance functions.- Matern class.- Exercises.- 2.8 Abelian and Tauberian theorems.- Exercises.- 2.9 Random fields with nonintegrable spectral densities.- Intrinsic random functions.- Semivariograms.- Generalized random fields.- Exercises.- 2.10 Isotropic autocovariance functions.- Characterization.- Lower bound on isotropic autocorrelation functions.- Inversion formula.- Smoothness properties.- Matern class.- Spherical model.- Exercises.- 2.11 Tensor product autocovariances.- Exercises.- 3 Asymptotic Properties of Linear Predictors.- 3.1 Introduction.- 3.2 Finite sample results.- Exercise.- 3.3 The role of asymptotics.- 3.4 Behavior of prediction errors in the frequency domain.- Some examples.- Relationship to filtering theory.- Exercises.- 3.5 Prediction with the wrong spectral density.- Examples of interpolation.- An example with a triangular autocovariance function.- More criticism of Gaussian autocovariance functions.- Examples of extrapolation.- Pseudo-BLPs with spectral densities misspecified at high frequencies.- Exercises.- 3.6 Theoretical comparison of extrapolation and ointerpolation.- An interpolation problem.- An extrapolation problem.- Asymptotics for BLPs.- Inefficiency of pseudo-BLPs with misspecified high frequency behavior.- Presumed mses for pseudo-BLPs with misspecified high frequency behavior.- Pseudo-BLPs with correctly specified high frequency behavior.- Exercises.- 3.7 Measurement errors.- Some asymptotic theory.- Exercises.- 3.8 Observations on an infinite lattice.- Characterizing the BLP.- Bound on fraction of mse of BLP attributable to a set of frequencies.- Asymptotic optimality of pseudo-BLPs.- Rates of convergence to optimality.- Pseudo-BLPs with a misspecified mean function.- Exercises.- 4 Equivalence of Gaussian Measures and Prediction.- 4.1 Introduction.- 4.2 Equivalence and orthogonality of Gaussian measures.- Conditions for orthogonality.- Gaussian measures are equivalent or orthogonal.- Determining equivalence or orthogonality for periodic random fields.- Determining equivalence or orthogonality for nonperiodic random fields.- Measurement errors and equivalence and orthogonality.- Proof of Theorem 1.- Exercises.- 4.3 Applications of equivalence of Gaussian measures to linear prediction.- Asymptotically optimal pseudo-BLPs.- Observations not part of a sequence.- A theorem of Blackwell and Dubins.- Weaker conditions for asymptotic optimality of pseudo-BLPs.- Rates of convergence to asymptotic optimality.- Asymptotic optimality of BLUPs.- Exercises.- 4.4 Jeffreys's law.- A Bayesian version.- Exercises.- 5 Integration of Random Fields.- 5.1 Introduction.- 5.2 Asymptotic properties of simple average.- Results for sufficiently smooth random fields.- Results for sufficiently rough random fields.- Exercises.- 5.3 Observations on an infinite lattice.- Asymptotic mse of BLP.- Asymptotic optimality of simple average.- Exercises.- 5.4 Improving on the sample mean.- Approximating
$$\int_0^1 {\exp } (ivt)dt$$.- Approximating
$$\int_{<!-- -->{<!-- -->{[0,1]}^d}} {\exp (i{\omega ^T}x)} dx$$
in more than one dimension.- Asymptotic properties of modified predictors.- Are centered systematic samples good designs?.- Exercises.- 5.5 Numerical results.- Exercises.- 6 Predicting With Estimated Parameters.- 6.1 Introduction.- 6.2 Microergodicity and equivalence and orthogonality of Gaussian measures.- Observations with measurement error.- Exercises.- 6.3 Is statistical inference for differentiable processes possible?.- An example where it is possible.- Exercises.- 6.4 Likelihood Methods.- Restricted maximum likelihood estimation.- Gaussian assumption.- Computational issues.- Some asymptotic theory.- Exercises.- 6.5 Matern model.- Exercise.- 6.6 A numerical study of the Fisher information matrix under the Matern model.- No measurement error and?unknown.- No measurement error and?known.- Observations with measurement error.- Conclusions.- Exercises.- 6.7 Maximum likelihood estimation for a periodic version of the Matern model.- Discrete Fourier transforms.- Periodic case.- Asymptotic results.- Exercises.- 6.8 Predicting with estimated parameters.- Jeffreys's law revisited.- Numerical results.- Some issues regarding asymptotic optimality.- Exercises.- 6.9 An instructive example of plug-in prediction.- Behavior of plug-in predictions.- Cross-validation.- Application of Matern model.- Conclusions.- Exercises.- 6.10 Bayesian approach.- Application to simulated data.- Exercises.- A Multivariate Normal Distributions.- B Symbols.- References.
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