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David W. Meek

Abstract

The empirical semivariogram for Clark's adit-silver series has been the subject of several publications. Its use in the literature along with some other discussed considerations makes this series a suitable selection for a classroom or workshop semivariogram modeling exercise. My emphasis in this exercise is on estimating the scale of fluctuation (8). Alternative unbounded, bounded asymptotic, and bounded transitional models are developed via weighted least-squares estimation for both regular and integral semivariogram parameterizations (ISV). Results are compared with Clark's recommendation along with some other traditional models, nonparametric models, and ad hoc numerical methods. When a given model fits well using the regular method, generally the ISV does also. When a given model fits poorly using the regular method, however, generally the ISV form fits much worse, or gives unrealistic parameter estimates, or diverges. While an unbounded rational polynomial exponential performs well and presents some interesting existence considerations, for practical purposes the series can be considered bounded and a hyperbolic tangent is selected as the best performing simple parameterization. The ISV for the hyperbolic tangent gives parameter and 8 estimates closest to ad hoc independent values for them. In the spirit of non parametric models, however, splined-line segments can perform extremely well if parameter parsimony and parameter interpretation are not deemed important considerations by a given modeler.

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Apr 29th, 5:10 PM

ANOTHER LOOK AT CLARK'S ADIT-SILVER SERIES

The empirical semivariogram for Clark's adit-silver series has been the subject of several publications. Its use in the literature along with some other discussed considerations makes this series a suitable selection for a classroom or workshop semivariogram modeling exercise. My emphasis in this exercise is on estimating the scale of fluctuation (8). Alternative unbounded, bounded asymptotic, and bounded transitional models are developed via weighted least-squares estimation for both regular and integral semivariogram parameterizations (ISV). Results are compared with Clark's recommendation along with some other traditional models, nonparametric models, and ad hoc numerical methods. When a given model fits well using the regular method, generally the ISV does also. When a given model fits poorly using the regular method, however, generally the ISV form fits much worse, or gives unrealistic parameter estimates, or diverges. While an unbounded rational polynomial exponential performs well and presents some interesting existence considerations, for practical purposes the series can be considered bounded and a hyperbolic tangent is selected as the best performing simple parameterization. The ISV for the hyperbolic tangent gives parameter and 8 estimates closest to ad hoc independent values for them. In the spirit of non parametric models, however, splined-line segments can perform extremely well if parameter parsimony and parameter interpretation are not deemed important considerations by a given modeler.