Abstract
A parametric surface estimation algorithm is examined. The algorithm is a perfect interpolator. The points surrounding the point to be estimated are weighted according to the length of their paths from the point to be estimated, and not their Euclidean distance from that point. The algorithm is capable of estimating surfaces that are not functions and twist, turn, and fold, into the three dimensional space in any direction. The big advantage of this family of algorithms is that they do not require the process, the data came from, to satisfy the intrinsic hypothesis, or be second order stationary. Furthermore, they do not require equal distance between sampling points or continuity of the first or second derivatives. From the computational point of view they do not require matrix inversion. This family of methods is therefore robust. Given any set of points in the three dimensional space we show that this family of interpolators converges and always produces a surface. The disadvantage of this method is that, due to the lack of strict assumptions, it is difficult to calculate the error of estimation. Under the assumption of stationarity we calculate the error of the estimate, produced by interpolating with our method. Thus under the assumption of stationarity our method can be compared with kriging.
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© 1993 Kluwer Academic Publishers
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Yfantis, E.A., Flatman, G.T., Miller, F. (1993). Parametric Surface Estimation. In: Soares, A. (eds) Geostatistics Tróia ’92. Quantitative Geology and Geostatistics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1739-5_13
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DOI: https://doi.org/10.1007/978-94-011-1739-5_13
Publisher Name: Springer, Dordrecht
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