On optimal allocations for estimating the surface of a random field |
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| Authors: | Thomas Müller-Gronbach Rainer Schwabe |
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| Institution: | 1. Freie Universit?t Berlin, 1. Mathematisches Institut Arnimallee 2-6, 14195, Berlin, Germany
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| 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.
work supported by 313/ARC/VII/93/151 of the DAAD
work supported by Ku719/2-1 of the DFG |
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| Keywords: | Approximation of random fields integrated mean squared error reproducing kernel Hilbert space product type Sacks-Ylvisaker conditions asymptotically optimal designs |
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