Robust Resampling Confidence Intervals for Empirical Variograms |
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Authors: | Robert Graham Clark Samuel Allingham |
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Institution: | (1) Department of Engineering for Crop Production, Leibniz-Institute for Agricultural Engineering, Max-Eyth-Allee 100, D-14469 Potsdam, Germany;(2) Laboratory of Geo-Information Science and Remote Sensing, Wageningen University, 47, 6700 AA Wageningen, The Netherlands |
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Abstract: | The variogram function is an important measure of the spatial dependencies of a geostatistical or other spatial dataset. It
plays a central role in kriging, designing spatial studies, and in understanding the spatial properties of geological and
environmental phenomena. It is therefore important to understand the variability attached to estimates of the variogram. Existing
methods for constructing confidence intervals around the empirical variogram either rely on strong assumptions, such as normality
or known variogram function, or are based on resampling blocks and subject to edge effect biases. This paper proposes two
new procedures for addressing these concerns: a quasi-block-bootstrap and a quasi-block-jackknife. The new methods are based
on transforming the data to decorrelate it based on a fitted variogram model, resampling blocks from the decorrelated data,
and then recorrelating. The coverage properties of the new confidence intervals are compared by simulation to a number of
existing resampling-based intervals. The proposed quasi-block-jackknife confidence interval is found to have the best properties
of all of the methods considered across a range of scenarios, including normally and lognormally distributed data and misspecification
of the variogram function used to decorrelate the data. |
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