Abstract
In general, the construction of optimal designs is apparently a difficult task for the approximation of a random field indexed by more than one dimension. Besides the rate of convergence of the minimum achievable error hardly anything is known until now. However, if there is an immanent structure present in the random field, then, taking this structure into account, improved estimates can be obtained. For this situation we present adequate designs which show, at least, a nearly optimal performance.
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work supported by 313/ARC/VII/93/151 of the DAAD
work supported by Ku719/2-1 of the DFG
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Müller-Gronbach, T., Schwabe, R. On optimal allocations for estimating the surface of a random field. Metrika 44, 239–258 (1996). https://doi.org/10.1007/BF02614069
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DOI: https://doi.org/10.1007/BF02614069