华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (2): 31-36,5.

• 数学 统计学 • 上一篇    下一篇

熵和对称损失函数下MINQUE和简单估计的比较(英)

艾摩尔   

  1. 华东师范大学 统计系,上海 200062
  • 收稿日期:2002-09-04 修回日期:2002-10-11 出版日期:2004-06-25 发布日期:2004-06-25
  • 通讯作者: 艾摩尔

Comparison of MINQUE and Simple Estimators under Entropy and Symmetry Loss Functions

Abdul-Hussein Saber AL-MOUEL   

  1. Department of Mathematical Statistics, East China Normal University, Shanghai 200062, China
  • Received:2002-09-04 Revised:2002-10-11 Online:2004-06-25 Published:2004-06-25
  • Contact: Abdul-Hussein Saber AL-MOUEL

摘要: 在熵损失和对称损失函数下,研究了多元线性模型协方差矩阵的MINQUE估计和简单估计的比较问题,其中多元线性模型的设计矩阵和离散矩阵可以不满秩.并证明了,在熵损失函数下,MINQUE估计总是优于简单估计.

关键词: 多元线性模型, MINQUE估计, 风险, 熵损失函数, 对称损失函数, 多元线性模型, MINQUE估计, 风险, 熵损失函数, 对称损失函数

Abstract: This paper considers comparison of MINQUE and simple estimator of Σ in the multivariate normal linear model Y~N(XB, Σ×V) under the risk of entropy loss function and symmetry loss function criterion, where the design matrix X need not have full rank and the dispersion matrix V can be singular. It is interested to prove that MINQUE is superior to simple estimator under Entropy loss function.

Key words: MINQUE, risk function, entropy loss function, symmetry loss function, multivariate linear model, MINQUE, risk function, entropy loss function, symmetry loss function

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