正交平衡区组设计矩阵象的概念及其基本定理

给出了正交平衡区组设计(或广义正交表)的矩阵象的概念及例子,证明了矩阵象的几个基本定理,得出了正交平衡区组设计的正交性等价于矩阵象的正交性的重要结论,从而为利用正交平衡区组设计进行数据分析提供了理论依据.     

发射物体到指定位置的稳健性参数设计

发射物体到指定位置的稳健性参数设计是稳健性设计中的经典例子之一,也是导弹控制理论中的一个常用模型.但就是对这个经典例子,许多教科书给出的并非最优解.用创立的求解稳定中心的方法(称为全局-局部分析方法或者GL算法Global-Local Algorithm),得出了比历史上更好的稳定中心,并由此引出了许多哲学层面的问题.     

A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2

Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.     

一类试验次数为4p2的非对称正交表的构造

Nowadays orthogonal arrays play important roles in statistics,computer science, coding theory and cryptography.The usual difference matrices are essential for the con- struction of many mixed orthogonal arrays.But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices.In order to construct these asymmetrical orthogonal arrays,a class of special matrices,so-called generalized difference matrices,were discovered by Zhang(1989,1990, 1993) by the orthogonal decompositions of projective matrices.In this article,an interesting equivalent relationship between the orthogonal arrays and the generalized difference matri- ces is presented.As an application,a family of orthogonal arrays of run sizes 4p~2,such as L_(36)(6~13~42~(10)),are constructed.     

条件密度近邻－核估计的逼近速度

本文首先研究了条件密度函数近邻－核估计的误差分布的正态逼近精度,然后利用随机加权法构造了近邻－核估计的随机加权统计量,获得了随机加权逼近精度。