统计研究 ›› 2013, Vol. 30 ›› Issue (3): 101-105.

• 论文 • 上一篇    下一篇

三个多元正态总体在简单半序约束下均值估计

罗平 李树有   

  • 出版日期:2013-03-15 发布日期:2013-03-13

Estimation of Means of Three Multivariate Normal Populations with Simple Order Restriction

Luo Ping & Li Shuyou   

  • Online:2013-03-15 Published:2013-03-13

摘要: 多元保序回归理论对统计学中研究多维参数在序约束下的估计理论起着关键性作用。本文讨论了当协方差矩阵已知,在简单半序约束下,对三个多元正态总体均值的估计问题,给出了估计的算法。并证明了在多元均方损失条件下,给出的均值估计优于无序约束的均值估计。

关键词: 多元正态均值, 简单半序约束, 极大似然估计, 风险函数, 算法

Abstract: Multivariate isotonic regression theory plays a key role in the study of statistical estimation theory of multivariate parameters under order restriction. In this paper, estimation of the means of three multivariate normal populations under simple order restriction is discussed, while the covariance matrices are known, and corresponding algorithm of estimation is given. It is also demonstrated that, under the condition of generalized square loss, the new estimation of means is better than that under disordered restriction.

Key words: Multivariate Normal Mean, Simple Order Restriction, Maximum Likelihood Estimation, Risk Function, Algorithm