Interval-valued random functions and the kriging of intervals |
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Authors: | Phil Diamond |
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Institution: | (1) Department of Mathematics, University of Queensland, 4067 St. Lucia, Qld., Australia |
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Abstract: | Estimation procedures using data that include some values known to lie within certain intervals are usually regarded as problems of constrained optimization. A different approach is used here. Intervals are treated as elements of a positive cone, obeying the arithmetic of interval analysis, and positive interval-valued random functions are discussed. A kriging formalism for interval-valued data is developed. It provides estimates that are themselves intervals. In this context, the condition that kriging weights be positive is seen to arise in a natural way. A numerical example is given, and the extension to universal kriging is sketched. |
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Keywords: | interval-valued data random function kriging |
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