Abstract
For equally spaced observations from a one-dimensional, stationary, Gaussian random function, the characteristic function of the usual variogram estimator\(\hat \gamma k\) for a fixed lag k is derived. Because the characteristic function and the probability density function form a Fourier integral pair, it is possible to tabulate the sampling distribution of a function of a\(\hat \gamma k\) using either analytic or numerical methods. An example of one such tabulation is given for an underlying model that is simple transitive.
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Davis, B.M., Borgman, L.E. Some exact sampling distributions for variogram estimators. Mathematical Geology 11, 643–653 (1979). https://doi.org/10.1007/BF01031889
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DOI: https://doi.org/10.1007/BF01031889