Abstract
In this article, kriging is equated with spatial optimal linear prediction, where the unknown random-process mean is estimated with the best linear unbiased estimator. This allows early appearances of (spatial) prediction techniques to be assessed in terms of how close they came to kriging.
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References
Cressie, N., 1991, Statistics for spatial data: Wiley, New York (forthcoming).
Fairfield Smith, H., 1936, A discriminant function for plant selection: Annals of Eugenics, v. 7, p. 240–250.
Gandin, L. S., 1963, Objective analysis of meteorological fields: Gidrometeorologicheskoe Izdatel'stvo (GIMIZ), Leningrad (translated by Israel Program for Scientific Translations, Jerusalem, 1965, 238 pp.).
Gauss, C. F., 1809, Theoria motus corporum celestium: Perthes et Besser, Hamburg (tranlslated as Theory of motion of the heavenly bodies moving about the sun in conic sections, trans. C. H. Davis: Little, Brown, Boston, 1857).
Goldberg, A. S., 1962, Best linear unbiased prediction in the generalized linear regression model: J. Am. Stat. Assoc., v. 57, p. 369–375.
Hazel, L. N., 1943. The genetic basis for constructing selection indexes: Genetics, v. 28, p. 476–490.
Hemyari, P., and Nofziger, D. L., 1987, Analytical solution for punctual kriging in one dimension: Soil Sci. Soc. Am. J., 51, p. 268–269.
Henderson, C. R., 1963, Selection index and expected genetic advance,in Statistical genetics and plant breeding, W. D. Hanson and H. F. Robinson (Eds.): National Research Council Publication 982, National Academy of Sciences, Washington, D.C., p. 141–163.
Journel, A. G., and Huijbregts, C. J., 1978, Mining geostatics: Academic Press, London, 600 pp.
Kolmogorov, A. N., 1941a, Interpolation and extrapolation of stationary random sequences: Izvestiia Akademii Nauk SSR, Seriia Matematicheskaia, v. 5, p. 3–14 (translation, Memo RM-3090-PR, Rand Corporation, Santa Monica, California, 1962, 14 pp.).
Kolmogorov, A. N., 1941b, The local structure of turbulence in an incompressible fluid at very large Reynolds numbers: Doklady Akademii Nauk SSR, v. 30, p. 301–305 (reprinted in Turbulence: classic papers of statistical theory, S. K. Friedlander and L. Topping (Ed.): Interscience Publishers, New York, 1961, p. 151–155).
Krige, D. G., 1951, A statistical approach to some basic mine valuation problems on the Witwatersrand: J. Chem. Metal. Min. Soc. South Africa, v. 52, p. 119–139.
Krige, D. G., 1962a, Effective pay limits for selective mining: J. South Africa Inst. Min. Metal., v. 62, p. 345–363.
Krige, D. G., 1962b, Economic aspects of stoping through unpayable ore: J. South African Inst. Min. Metal., v. 62, p. 364–374.
Krige, D. G., 1966, Two-dimensional weighted moving average trend surfaces for ore valuation,in Symposium on mathematical statistics and computer applications in ore valuation: Johannesberg, South Africa, 1966. Special issue of J. South African Inst. Min. Metal., p. 13–79.
Krige, D. G., 1978, Lognormal-de Wijsian geostatistics for ore evaluation: South African Institute of Mining and Metallurgy Monograph Series, Johannesburg, 50 pp.
Krige, D. G., and Ueckermann, H. J., 1963, Value contours and improved regression techniques for ore reserve valuations: J. South African Inst. Min. Metal., v. 63, p. 429–452.
Legendre, A. M., 1805, Nouvelles méthodes pour la détermination des orbites des cométes: Courcier, Paris, 80 pp.
Matern, B., 1960, Spatial variation: Meddelanden fran Statens Skogsforskningsinstitute, v. 49, 144 pp.
Matheron, G., 1962, Traité de geostatisque appliquée, vol. I: Memoires du Bureau de Recherches Géologiques et Miniéres, no. 14, Editions Technip, Paris, 333 pp.
Matheron, G., 1963a, Traité de geostatistique appliquée, vol. II, Le krigeage: Memoires du Bureau de Recherches Géologiques et Miniéres, no. 24, Editions Bureau de Recherche Géologiques et Miniéres, Paris, 171, pp.
Matheron, G., 1963b, Principles of geostatistics: Economic Geol., v. 58, p. 1246–1266.
Matheron, G., 1967, Kriging or polynomial interpolation procedures?: Trans. Canad. Inst. Min. Metal., v. 70, p. 240–244.
Moritz, H., 1963, Statistische methoden in der gravimetrischen geodasie: Zeitschrift fur Vermessungswesen, v. 88, p. 409–416.
Ord, J. K., 1983, Kriging, entry,in Encyclopedia of statistical sciences, vol. 4, S. Kotz and N. Johnson (Eds.): Wiley, New York, p. 411–413.
Stigler, S. M., 1980, Stigler's law of eponymy: Trans. New York Acad. Sci. Series 2, v. 39 (Merton Festschrift Vol., ed. by T. Gieryn), p. 147–158.
Thompson, P. D., 1956, Optimum smoothing of two-dimensional fields: Tellus, v. 8, p. 384–393.
Whitten, E. H. T., 1966, The general linear equation in prediction of gold content in Witwatersrand rocks, South Africa,in Symposium on mathematical statistics and computer applications in ore valuation: Johannesberg, South Africa, 1966; special issue of J. South African Inst. Min. Metal., p. 124–147.
Whittle, P., 1963, Prediction and regulation by linear least-square methods: van Nostrand, Princeton, 141 pp.
Wiener, N., 1949, Extrapolation, interpolation and smoothing of stationary time series: MIT Press, Cambridge, Massachusetts, 158 pp.
Wold, H., 1938, A. study in the analysis of stationary time series: Almqvist and Wiksells, Uppsala, 211 pp.
Yaglom, A. M., 1957, Some classes of random fields inn-dimensional space, related to stationary random processes: Theory Prob. Appl., v. 2, p. 273–320.
Yaglom, A. M., 1962, An introduction to the theory of stationary random functions: Prentice-Hall (as of 1973, published by Dover, New York, 235 pp.).
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Cressie, N. The origins of kriging. Math Geol 22, 239–252 (1990). https://doi.org/10.1007/BF00889887
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DOI: https://doi.org/10.1007/BF00889887