数学物理学报 ›› 2000, Vol. 20 ›› Issue (zk): 625-632.

• 论文 • 上一篇    下一篇

关于链模型的回归系数与协方差阵元素的关系

李开灿 耿直   

  1. 北京大学概率统计系 北京100871
  • 收稿日期:1998-06-15 出版日期:2000-11-10 发布日期:2000-11-10

The relation of the regression coefficients of chain model and elments of the covariance matrix

LI Kai-Can |GENG-Zhi   

  1. beijing university statistics department,beijing 100871
  • Received:1998-06-15 Online:2000-11-10 Published:2000-11-10

摘要:

该文以数学公式的形式严格定义了[1][2]提出的多元链回归模型,块回归链模型.导出了这两类模型的回归系数用协方差矩阵元素表式的解析表达式.这些都去掉了[1][2]要求正态分布的假设.它们对图模型的理论研究及其应用都是很有价值的。最后本文还对一种块链模型讨论了它的回归系数与协方差阵元素所满足约束的互相对应关系.

关键词: 多元回归链模型 , 块回归链模型 , 协方差阵 , 偏协方差阵 , 既约零型

Abstract:

In this paper,we have exactly defined the general formulae for the multivariate  regression chain model and the block regression chain model proposedinpaper [1]and [2].When the random vector in the models does not follow a multivariate normal distribution,regression coefficients of both models are represented in terms of the elements ofthe covariance matrix.Those extend the results of[1]and[2]tothe cases of general distributions.Further we show the relationship between the coefficients of a special block regression chain model and the elements of the covariance matrix.

Key words: Multivariate regression chain model, Partial variance matrix, Reduciblezero pattern

中图分类号: 

  • 62J