基于一般正交表的空间填充设计的中心极限定理
A central limit theorem for general orthogonal array based space-filling designs
摘要：
基于正交表的空间填充设计（Owen [Statistist. Sinica 2（1992 a）439-452]; Tang [J. Amer. Statistist. Assoc.88（1993）1392-1397]）已经在计算机实验、数值积分、随机最优化和不确定性量化中变得流行。作为对普通拉丁超立方体设计的改进，这些设计实现了多维分层。如果基础正交阵列具有强度$t$，则此类设计实现了高达$t$维度的均匀性。现有的中心极限定理仅限于这些设计与强度两个正交表的基础上，只有二维分层。我们发展了一个新的中心极限定理，这些设计，具有分层在任意多维与正交表的一般强度。这一结果对于在各种统计应用中为此类设计建立置信度声明是有用的。
英文摘要：
Orthogonal array based space-filling designs (Owen [Statist. Sinica 2 (1992a) 439-452]; Tang [J. Amer. Statist. Assoc. 88 (1993) 1392-1397]) have become popular in computer experiments, numerical integration, stochastic optimization and uncertainty quantification. As improvements of ordinary Latin hypercube designs, these designs achieve stratification in multi-dimensions. If the underlying orthogonal array has strength $t$, such designs achieve uniformity up to $t$ dimensions. Existing central limit theorems are limited to these designs with only two-dimensional stratification based on strength two orthogonal arrays. We develop a new central limit theorem for these designs that possess stratification in arbitrary multi-dimensions associated with orthogonal arrays of general strength. This result is useful for building confidence statements for such designs in various statistical applications.
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