Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications

Song-Nan Liu, Min-Qian Liu and Jin-Yu Yang ()
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Song-Nan Liu: School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China
Min-Qian Liu: School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China
Jin-Yu Yang: School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China

Mathematics, 2023, vol. 11, issue 6, 1-27

Abstract: For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on s 2 × s or s × s 2 grids, and most column pairs satisfy stratifications on s 2 × s 2 grids. Moreover, many column pairs can achieve stratifications on s 4 × s 2 and s 2 × s 4 grids. Furthermore, the obtained space-filling ODs can have s 6 levels, s 4 levels, and mixed levels, as required for different needs.

Keywords: Latin hypercube design; orthogonal array; orthogonality; rotation; stratification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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