A0720
Title: A projection space-filling criterion and related optimality results
Authors: Chenlu Shi - Colorado State University (United States) [presenting]
Hongquan Xu - University of California Los Angeles (United States)
Abstract: Computer experiments call for space-filling designs. Recently, a minimum aberration type space-filling criterion was proposed to rank and assess a family of space-filling designs, including Latin hypercubes and strong orthogonal arrays. It aims to capture a design's space-filling properties when projected onto subregions of various sizes. The dimension aside from the sizes of subregions by proposing first an expanded space-filling hierarchy principle and then a projection space-filling criterion as per the new principle are also considered. When projected onto subregions of the specific size, the proposed criterion ranks designs via sequentially maximizing the space-filling properties on equally-sized subregions in lower dimensions to higher dimensions, while the minimum aberration type space-filling criterion compares designs by maximizing the aggregate space-filling properties on multidimensional subregions of the same size. Further, the construction of the optimal space-filling designs is considered under the proposed criterion. Although many algorithms have been proposed for generating space-filling designs, it is well-known that they often deteriorate rapidly in performance for large designs. In the present paper, some theoretical optimality results and characterize several classes of strong orthogonal arrays of strength three that are the most space-filling are developed.
