A Comparison of Spatial Semivariogram Estimators and Corresponding Ordinary Kriging Predictors

REFERENCES

• Clark , I. 1979 . Practical Geostatistics London : Applied Science. .
   Google Scholar
• Cressie , N. 1984 . “Towards Resistant Geostatistics”. ” . In Geostatistics for Natural Resource Characterization Edited by: Verly , G. , David , M. , Journel , A. G. and Marechal , A. 21 – 44 . Dordrecht : Reidel. .
   Google Scholar
• Cressie , N. 1985 . “Fitting Variogram Models by Weighted Least Squares,” . Mathematical Geology , 17 : 563 – 586 .
   Google Scholar
• Cressie , N. 1986 . “Kriging Nonstationary Data,” . Journal of the American Statistical Association , 81 : 625 – 634 .
   Web of Science ®Google Scholar
• Cressie , N. 1987 . “A Nonparametric View of Generalized Covariances for Kriging,” . Mathematical Geology , 19 : 425 – 449 .
   Google Scholar
• Cressie , N. , Gotway , C. A. and Grondona , M. O. 1990 . “Spatial Prediction From Networks,” . Chemometrics and Intelligent Laboratory Systems , 1 : 251 – 271 .
   Web of Science ®Google Scholar
• Cressie , N. and Hawkins , D. M. 1980 . “Robust Estimation of the Variogram.” . Mathematical Geology , 12 : 115 – 125 .
   Google Scholar
• Davis , M. W. 1987 . “Production of Conditional Simulations via the LU Triangular Decomposition of the Covariance Matrix,” . Mathematical Geology , 19 : 91 – 98 .
   Google Scholar
• Delfiner , P. 1976 . “Linear Estimation of Nonstationary Spatial Phenomena”. ” . In Advanced Geostatistics in the Mining Industry Edited by: Guarascio , M. , David , M. and Huijbregts , C. 49 – 68 . Dordrecht : Reidel. .
   Google Scholar
• Delfiner , P. , Renard , D. and Chiles , J. P. 1978 . BLUEPACK-3D Manual Fontainebleu , , France : Centre de Geostatistique. .
   Google Scholar
• Diamond , P. and Armstrong , M. 1984 . “Robustness of Variograms and Conditioning of Kriging Matrices,” . Mathematical Geology , 16 : 809 – 822 .
   Google Scholar
• Emerson , J. D. and Hoaglin , D. C. 1983 . “Analysis of Two-Way Tables by Medians”. ” . In Understanding Robust and Exploratory Data Analysis Edited by: Hoaglin , D. C. , Mosteller , F. and Tukey , J. W. 166 – 210 . New York : John Wiley. .
   Google Scholar
• Handcock , M. S. 1988 . “Likelihood Based Estimation of Covariance Functions of Spatial Gaussian Random Fields for the Purposes of Prediction,” University of Chicago, Dept. of Statistics. . unpublished manuscript
   Google Scholar
• Hoeksema , R. J. and Kitanidis , P. K. 1985 . “Analysis of the Spatial Structure of Properties of Selected Aquifers,” . Water Resources Research , 21 : 563 – 572 .
   Web of Science ®Google Scholar
• Journel , A. G. and Huijbregts , C. J. 1978 . Mining Geostatistics London : Academic Press. .
   Google Scholar
• Kennedy , W. J. and Gentle , J. E. 1980 . Statistical Computing New York : Marcel Dekker. .
   Google Scholar
• Kitanidis , P. K. 1983 . “Statistical Estimation of Polynomial Generalized Covariance Functions and Hydrologic Applications,” . Water Resources Research , 19 : 909 – 921 .
   Web of Science ®Google Scholar
• Mardia , K. V. and Marshall , R. J. 1984 . “Maximum Likelihood Estimation of Models for Residual Covariance in Spatial Regression,” . Biometrika , 71 : 135 – 146 .
   Web of Science ®Google Scholar
• Mardia , K. V. and Watkins , A. J. 1989 . “On Multimodality of the Likelihood in the Spatial Linear Model,” . Biometrika. , 76 : 289 – 295 .
   Web of Science ®Google Scholar
• Matheron , G. 1963 . “Principles of Geostatistics,” . Economic Geology. , 58 : 1246 – 1266 .
   Google Scholar
• Matheron , G. 1973 . “The Intrinsic Random Functions and Their Applications,” . Advances in Applied Probability , 5 : 437 – 468 .
   Google Scholar
• Patterson , H. D. and Thompson , R. 1971 . “Recovery of Interblock Information When Block Sizes Are Unequal,” . Biometrika , 58 : 545 – 554 .
   Web of Science ®Google Scholar
• Ripley , B. D. 1981 . Spatial Statistics. New York : John Wiley. .
   Google Scholar
• Starks , T. H. and Fang , J. H. 1982 . “On the Estimation of the Generalized Covariance Function,” . Mathematical Geology. , 14 : 57 – 64 .
   Google Scholar
• Stein , M. L. 1987 . “Minimum Norm Quadratic Estimation of Spatial Variograms,” . Journal of the American Satistical Association , 82 : 765 – 772 .
   Web of Science ®Google Scholar
• Stein , M. L. and Handcock , M. S. 1989 . “Some Asymptotic Properties of Kriging When the Covariance Function is Misspecified,” . Mathematical Geology , 21 : 171 – 190 .
   Google Scholar
• Swallow , W. H. and Monahan , J. F. 1984 . “A Monte Carlo Comparison of ANOVA, MIVOUE, REML, and ML Estimators of Variance Components,” . Technometrics. , 26 : 47 – 57 .
   Web of Science ®Google Scholar
• Warnes , J. J. and Ripley , B. D. 1987 . “Problems With Likelihood Estimation of Covariance Functions of Spatial Gaussian Processes,” . Biometrika , 74 : 640 – 642 .
   Web of Science ®Google Scholar
• Zimmerman , D. L. 1986 . “A Random Field Approach to Spatial Experiments,” Iowa State University, Dept. of Statistics. . unpublished Ph.D. thesis
   Google Scholar
• Zimmerman , D. L. 1989 . “Computationally Exploitable Structure of Covariance Matrices and Generalized Covariance Matrices in Spatial Models,” . Journal of Statistical Computation and Simulation , 32 : 1 – 15 .
   Google Scholar
• Zimmerman , D. L. and Cressie , N. “Mean Squared Prediction Error in the Spatial Linear Model With Estimated Covariance Parameters,” . Annals of the Institute of Statistical Mathematics , 43 (in press)
   Web of Science ®Google Scholar