一类正交拉丁超立方体设计二维投影均匀性的研究
Research on Two-Dimensional Projection Uniformity for a Class of Orthogonal Latin Hypercube Designs
摘要: 正交拉丁超立方体设计(Orthogonal Latin hypercube designs, OLHDs)适用于计算机试验，是具有列正交性的一类空间填充设计。本文讨论了试验次数一般的一类正交拉丁超立方体设计在二维空间的投影均匀性，即在二维网格上的分层性质。结果表明该设计的所有列对都可以实现在
s ×
s网格分层；来自相同组连续不相邻的列对可以实现在
s ×
s2和
s2 ×
s网格上分层，某些列对还能实现在
s2 ×
s2网格上的分层。
Abstract: The Orthogonal Latin hypercube designs (OLHD), which is a class of space-filling designs with column orthogonality, is suitable for computer experiments. In this paper, the projection uniformity of a class of OLHDs with more general run sizes in two dimensions is discussed, i.e., the grid layering properties. The results show that the design can achieve stratifications on s × s grids in any two dimensions; most column pairs can achieve stratifications on finer s2 × s and s × s2 grids when the two columns are from the same group that are not adjacent to each other, and some column pairs achieve stratifications on s2 × s2 grids.
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