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Blackbox Kriging: Spatial Prediction without Specifying Variogram Models

Ronald Paul Barry and Jay M. Ver Hoef
Journal of Agricultural, Biological, and Environmental Statistics
Vol. 1, No. 3 (Sep., 1996), pp. 297-322
Stable URL: http://www.jstor.org/stable/1400521
Page Count: 26
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Blackbox Kriging: Spatial Prediction without Specifying Variogram Models
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Abstract

This article proposes a new approach to kriging, where a flexible family of variograms is used in lieu of one of the traditionally used parametric models. This nonparametric approach minimizes the problems of misspecifying the variogram model. The flexible variogram family is developed using the idea of a moving average function composed of many small rectangles for the one-dimensional case and many small boxes for the two-dimensional case. Through simulation, we show that the use of flexible piecewise-linear models can result in lower mean squared prediction errors than the use of traditional models. We then use a flexible piecewise-planar variogram model as a step in kriging the two-dimensional Wolfcamp Aquifer data, without the need to assume that the underlying process is isotropic. We prove that, in one dimension, any continuous variogram with a sill can be approximated arbitrarily close by piecewise-linear variograms. We discuss ways in which the piecewise-linear variogram models can be modified to improve the fit of the variogram estimate near the origin.

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