Two-dimensional projection uniformity for space-filling designs |
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Authors: | Sixu Liu Yaping Wang Fasheng Sun |
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Institution: | 1. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084 China;2. KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, 200062 China;3. KLAS and School of Mathematics and Statistics, Northeast Normal University, Jilin, 130024 China |
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Abstract: | We investigate a space-filling criterion based on -type discrepancies, namely the uniform projection criterion, aiming at improving designs' two-dimensional projection uniformity. Under a general reproducing kernel, we establish a formula for the uniform projection criterion function, which builds a connection between rows and columns of the design. For the commonly used discrepancies, we further use this formula to represent the two-dimensional projection uniformity in terms of the -distances of U-type designs. These results generalize existing works and reveal new links between the two seemingly unrelated criteria of projection uniformity and the maximin -distance for U-type designs. We also apply the obtained results to study several families of space-filling designs with appealing projection uniformity. Because of good projected space-filling properties, these designs are well adapted for computer experiments, especially for the case where not all the input factors are active. |
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Keywords: | Computer experiment discrepancy Latin hypercube maximin distance uniform projection design |
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