广义对称表的矩阵象和点估计  

Matrix Image and Point Estimates of Generalized Symmetrical Arrays

作　　者：白金峰 张应山 赵建立[3] BAI Jinfeng;ZHANG Yingshan;ZHAO Jianli(Faculty of Business,City University of Macao,Macao 999078,China;School of Statistics,Faculty of Economics and Management,East China Normal University,Shanghai 200241,China;School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]澳门城市大学商学院,中国澳门999078 [2]华东师范大学经济与管理学部统计学院,上海200241 [3]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2021年第1期1-10,共10页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(11301247);教育部高等学校博士学科点专项基金项目(200802691021)资助。

摘　　要：基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统对称多指标问题、对称非均匀性问题、对称非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明。广义对称性或广义对称分析方法,是许多学科关注的问题之一,在研究广义对称性问题时,构造广义对称表和正交幂等系统成为了研究广义对称性问题的基础。利用自由函数模型,根据正交幂等系统,采取对称置换不变性作为平衡指标,定义广义对称表的矩阵象,并给出对称分解项及其方差和贡献率的点估计。This series of articles based on“multilateral matrix theory”,inspired by the Eastern holistic thinking by trying to provide and improve a whole complex system to handle symmetrical multi-target problems,symmetrical non-uniformity problems,symmetrical nonlinear problems,a powerful mathematical tool from Global to Local issues and its rigorous theoretical analysis and proof.Generalized symmetry or generalized symmetry analysis method is one of the concerns in the study of generalized symmetry problems,the structure for both generalized symmetrical arrays and orthogonal idempotent systems is the basis of generalized symmetry problems.As the second series of papers,in this paper,using the free function model,according to the orthogonal idempotent system,adopting the symmetrical permutation invariability as a balance index,both the matrix image definition of generalized symmetrical arrays and the point estimates of symmetrical decomposition items are discussed.

关 键 词：广义对称表 正交幂等系统 自由函数模型 对称置换不变性 对称矩阵象 

分 类 号：O212.6[理学—概率论与数理统计]