Abstract tubes associated with perturbed polyhedra with applications to multidimensional normal probability computations
Abstract tubes associated with perturbed polyhedra with applications to multidimensional normal probability computations
复制标题
与扰动多面体相关的抽象管及其在多维正态概率计算中的应用
DOI：
10.1142/9789814383462_0010
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A. Hayter
中科院分区：
文献类型：
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作者：
S. Kuriki;Tetsuhisa Miwa;A. Hayter
令$ k $是由有限数量的线性不等式定义的封闭凸多面体。在本文中，我们完善了抽象管的理论（Naiman和Wynn，1997）与$ K $相关的$ K $时。特别是，我们专注于词汇图和外部方向的扰动。讨论了用于通过线性编程构建抽象管及其实现的算法。将抽象管用于扰动$ K $，结合Miwa，Hayter和Kuriki提出的递归集成技术（2003），我们表明，可以有效地计算多面体区域$ K $的多维正常概率。此外，抽象管和学生范围统计的分布函数作为数值示例。
Let $K$ be a closed convex polyhedron defined by a finite number of linear inequalities. In this paper we refine the theory of abstract tubes (Naiman and Wynn, 1997) associated with $K$ when $K$ is perturbed. In particular, we focus on the perturbation that is lexicographic and in an outer direction. An algorithm for constructing the abstract tube by means of linear programming and its implementation are discussed. Using the abstract tube for perturbed $K$ combined with the recursive integration technique proposed by Miwa, Hayter and Kuriki (2003), we show that the multidimensional normal probability for a polyhedral region $K$ can be computed efficiently. In addition, abstract tubes and the distribution functions of studentized range statistics are exhibited as numerical examples.