华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (5): 127-137.

• 应用数学与基础数学 • 上一篇    下一篇

对称性全局统计分析中的定理证明

潘长缘1, 马海南1, 2, 陈雪平1,张应山1   

  1. 1.华东师范大学 统计与精算学系,上海 200241; 2.浙江工业职业技术学院 基础部, 浙江 绍兴 312000
  • 收稿日期:2008-12-12 修回日期:2009-03-11 出版日期:2009-09-25 发布日期:2014-10-13
  • 通讯作者: 潘长缘

Proof procedure of some theories in statistical analysis of global symmetry (Chinese)

Pan Changyuan1,Ma Hainan1, 2, Chen Xueping1,Zhang Yingshan1   

  1. 1.Deptment of Statistics and Actuarial Science,East China Normal University,Shanghai 200241,China; 2.Fundamentals Department,Polytechnic Zhejiang Industry College,Shaoxing Zhejiang 312000,China
  • Received:2008-12-12 Revised:2009-03-11 Online:2009-09-25 Published:2014-10-13
  • Contact: Pan Changyuan

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摘要： 证明了对称性全局统计分析方法中的几个重要定理,保证了任意系统函数能够进行正交对称分解,确保了系统函数方差分解公式成立,这些是对称性全局统计分析方法的核心基石. 通过考察对称函数在整个系统函数中所起作用的大小,达到认识系统函数对称性的目的. 实例表明,将贡献率的Monte-Carlo计算值作为全局分析中对称函数的敏感 性度量指标,可以较好地刻画系统函数的对称性.

关键词: 类对称算符, 正交幂等系统, 对称函数, 全局统计分析, 类对称算符, 正交幂等系统, 对称函数, 全局统计分析

Abstract:

This research guaranteed orthogonal symmetry demonstration to any system function,ensured the formula of demonstration to system function variance.They are the kernel and foundation stone of statistical analysis of global symmetry.By studying how these symmetry functions work in the whole system function,the symmetry of system function can be understood better.As illustrated by the examples,it showed the symmetry of system function clearly by using the Monte-Carlo calculated value of contribution rate as the global sensitivity index of symmetry function.

Key words: systems of orthogonal idempotents, symmetry functions, global statistical analysis, Class idempotent function, systems of orthogonal idempotents, symmetry functions, global statistical analysis

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