Some exact optimal designs for linear covariance functions in one dimension

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Abstract
In the recent literature on computer experiments one of the problems considered is the choice of an appropriate design. For this purpose several algorithms have been proposed, but no explicit expressions are available. In the present paper we investigate linear covariance functions in one dimension, and show how exact optimal designs can be found for several design criteria. Linear in this context means that the obtained predictive function interpolates the observations linearly. Even though the results may not be of great practical importance, they should provide guidance for further work. An interpretation of the results according to the different distributional assumptions is given.

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