Two-dimensional projection uniformity for space-filling designs

作者：Liu, Sixu; Wang, Yaping; Sun, Fasheng^*

来源：CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2023, 51(1): 293-311.

DOI：10.1002/cjs.11686

• Computer experiment
• discrepancy
• Latin hypercube
• maximin distance
• uniform projection design

We investigate a space-filling criterion based on L2-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 Lp-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 Lp-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.

• 单位
  清华大学