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Theory and Method

Minimum Norm Quadratic Estimation of Spatial Variograms

Pages 765-772 | Received 01 Jan 1986, Published online: 12 Mar 2012

References

  • Baxter , G. 1956 . “A Strong Theorem for Gaussian Processes” . Proceedings of the American Mathematical Society , 7 : 522 – 527 .
  • Chung , K. L. 1974 . A Course in Probability Theory, , 2nd ed. , New York : Academic Press .
  • Cressie , N. 1985 . “Fitting Variogram Models by Weighted Least Squares” . Journal of the International Association for Mathematical Geology , 17 : 563 – 586 .
  • Cressie , N. 1986 . “Kriging Nonstationary Data” . Journal of the American Statistical Association , 81 : 625 – 634 .
  • Delfiner , P. “Linear Estimation of Non-stationary Spatial Phenomena” . Advanced Geostatistics in the Mining Industry, Proceedings of NATO A.S.I. Edited by: Gurascio , M. , David , M. and Huijbregts , C. pp. 49 – 68 . Dordecht : Reidel .
  • Harville , D. 1977 . “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems” . Journal of the American Statistical Association , 72 : 320 – 340 .
  • Hawkins , D. and Cressie , N. 1984 . “Robust Kriging—A Proposal” . Journal of the International Association for Mathematical Geology , 16 : 3 – 18 .
  • Hoeksema , R. J. and Kitanidis , P. K. 1984 . “An Application of the Geostatistical Approach to the Inverse Problem in Two-Dimensional Groundwater Modeling” . Water Resources Research , 20 : 1003 – 1020 .
  • Ibragimov , I. A. and Rozanov , Y. A. 1978 . Gaussian Random Processes , Edited by: Aries , A. B. New York : Springer-Verlag .
  • Journel , A. G. and Huijbregts , C. J. 1978 . Mining Geostatistics , New York : Academic Press .
  • Kitanidis , P. K. 1983 . “Statistical Estimation of Polynomial Generalized Covariance Functions and Hydrologic Applications” . Water Resources Research , 19 : 909 – 921 .
  • Kitanidis , P. K. 1985 . “Minimum-Variance Unbiased Quadratic Estimation of Covariances of Regionalized Variables” . Journal of the International Association for Mathematical Geology , 17 : 195 – 208 .
  • Kitanidis , P. K. and Lane , R. W. 1985 . “Maximum Likelihood Parameter Estimation of Hydrologic Spatial Processes by the Gauss—Newton Method” . Journal of Hydrology , 79 : 59 – 71 .
  • Mardia , K. V. and Marshall , R. J. 1984 . “Maximum Likelihood Estimation of Models for Residual Covariance in Spatial Regression” . Biometrika , 73 : 135 – 146 .
  • Matern , B. 1986 . Spatial Variation, , 2nd ed. , New York : Springer-Verlag .
  • Matheron , G. 1971 . The Theory of Regionalized Variables and Its Applications , Fontainebleau : Ecole de Mines .
  • Rao , C. R. 1971 . “Minimum Variance Quadratic Unbiased Estimation of Variance Components” . Journal of Multivariate Analysis , 1 : 445 – 456 .
  • Rao , C. R. 1972 . “Estimation of Variance and Covariance Components in Linear Models” . Journal of the American Statistical Association , 67 : 112 – 115 .
  • Rao , C. R. 1973 . Linear Statistical Inference and Its Applications, , 2nd ed. , New York : John Wiley .
  • Rao , C. R. 1979 . “MINQE Theory and Its Relation to ML and MML Estimation of Variance Components” . Sankhya , 41 : 138 – 153 . Ser. B
  • Ripley , B. D. 1981 . Spatial Statistics , New York : John Wiley .
  • Skorokhod , A. V. and Yadrenko , M. I. 1973 . “On Absolute Continuity of Measures Corresponding to Homogeneous Gaussian Fields” . Theory of Probability and Its Applications , 18 : 27 – 40 .
  • Stein , M. L. 1984 . “Estimation of Spatial Variability” , Stanford University, Dept. of Statistics . unpublished Ph.D. dissertation
  • Stein , M. L. 1986 . “Asymptotic Distributions of Minimum Norm Quadratic Estimators of Covariance Functions of Gaussian Random Fields” , University of Chicago, Dept. of Statistics . Technical Report 206
  • Stein , M. L. “Asymptotically Efficient Prediction of a Random Field With a Misspecified Covariance Function” . The Annals of Statistics , 16 (in press)
  • Wahba , G. and Wendelberger , J. 1980 . “Some New Mathematical Methods for Variational Objective Analysis Using Splines and Cross Validation” . Monthly Weather Review , 8 : 1122 – 1143 .

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