Abstract
Two approaches are considered to design experiments for a correlated random field when the objective is to obtain precise predictions over the whole experimental domain. Both take the uncertainty of the estimated parameters of the correlation structure of the random field into account. The first one corresponds to a compound D-optimality criterion for both the trend and covariance parameters. The second one relies on an approximation of the mean squared prediction error already proposed in the literature. It is conjectured, and shown on a paradigmatic example, that for some particular settings both approaches yield similar optimal designs, thereby revealing a sort of accordance between the two criteria for random fields. However, our example also shows that a strict equivalence theorem as in the uncorrelated case is not achievable. As a side issue we cast doubts on the ubiquity of equidistant space-filling designs.
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Acknowledgements
The article was mainly written during the first author’s research stay at the University of Nice-Sophia Antipolis and he wants to acknowledge its generous support. This work was also partially supported by a PHC Amadeus/OEAD Amadée grant FR11/2010. We are also grateful to an attentive referee for pointing out several omissions and typos.
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Müller, W.G., Pronzato, L., Waldl, H. (2012). Relations Between Designs for Prediction and Estimation in Random Fields: An Illustrative Case. In: Porcu, E., Montero, J., Schlather, M. (eds) Advances and Challenges in Space-time Modelling of Natural Events. Lecture Notes in Statistics(), vol 207. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17086-7_6
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