Continuity for Kriging with Moving Neighborhood
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By definition, kriging with a moving neighborhood consists in kriging each target point from a subset of data that varies with the target. When the target moves, data that were within the neighborhood are suddenly removed from the neighborhood. There is generally no screen effect, and the weight of such data goes suddenly from a non-zero value to a value of zero. This results in a discontinuity of the kriging map. Here a method to avoid such a discontinuity is proposed. It is based on the penalization of the outermost data points of the neighborhood, and amounts to considering that these points values are spoiled with a random error having a variance that increases infinitely when they are about to leave the neighborhood. Additional details are given regarding how the method is to be carried out, and properties are described. The method is illustrated by simple examples. While it appears to be similar to continuous kriging with a smoothing kernel, it is in fact based on a much simpler formalism.
KeywordsPenalized kriging Continuous kriging Kriging weights
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