一种构造基于类数独的分层空间填充设计的简单方法
A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs
摘要：
基于切片数独的空间填充设计和更一般的基于准切片正交数组的空间填充设计在几种情况下都是有用的试验设计，包括除了定量输入和交叉验证之外还使用分类的计算机实验。在这里，我们提供了一个简单的双正交准数独拉丁方，可用于生成切片的空间填充设计，实现均匀的一个和两个完整的设计和每个切片的二维投影的建设。还提供了基于这些构造的双正交准数独拉丁方的准切片正交表的构造，并且其又可以用于生成切片空间填充设计，该设计实现了完整设计的一维和二维投影的均匀性以及每个切片的二维投影的均匀性。这些构造对于实现和产生目前不广泛可用的设计尺寸和因素数量的范围是非常实用的。
英文摘要：
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced orthogonal array-based space-filling designs are useful experimental designs in several contexts, including computer experiments with categorical in addition to quantitative inputs and cross-validation. Here, we provide a straightforward construction of doubly orthogonal quasi-Sudoku Latin squares which can be used to generate sliced space-filling designs which achieve uniformity in one and two-dimensional projections for both the full design and each slice. A construction of quasi-sliced orthogonal arrays based on these constructed doubly orthogonal quasi-Sudoku Latin squares is also provided and can, in turn, be used to generate sliced space-filling designs which achieve uniformity in one and two-dimensional projections for the full design and and uniformity in two-dimensional projections for each slice. These constructions are very practical to implement and yield a spectrum of design sizes and numbers of factors not currently broadly available.
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