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Two-dimensional projection uniformity for space-filling designs
Authors:Sixu Liu  Yaping Wang  Fasheng Sun
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
Abstract:We investigate a space-filling criterion based on L 2 -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 L p -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 L p -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.
Keywords:Computer experiment  discrepancy  Latin hypercube  maximin distance  uniform projection design
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