不完全椭球约束下多元线性模型线性估计的可容许性(英文)  

Admissibility of Linear Estimators in Multivariate Linear Models with Respect to an Incomplete Ellipsoidal Restriction

作　　者：吴鑑洪[1] 

机构地区：[1]浙江工商大学统计与数学学院,杭州310018

出　　处：《应用概率统计》2009年第5期513-518,共6页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the Youth Talent Foundation of Zhejiang Gongshang University (Q09-12)

摘　　要：本文研究了多元线性模型当未知参数受不完全椭球约束tr(Θ-Θ1) N(Θ-Θ1) ≤σ2时线性估计的可容许性问题. 具体而言, 我们研究了约束tr(Θ-Θ1) N(Θ-Θ1) ≤σ2中N和非中心点Θ1对线性估计的可容许性的影响. 主要结果表明在两个不同的不完全椭球约束条件tr(Θ-Θ1) N(Θ-Θ1) ≤σ2与tr(Θ-Θ2) N(Θ-Θ2) ≤σ2下, 当Θ1和Θ2满足一定的关系时, 可容许的齐次线性估计类是相同的.This paper studies the admissibility of linear estimators in multivariate linear models with respect to an incomplete ellipsoidal restriction tr（Θ - Θ1）′N（Θ - Θ1） ≤ σ^2. Specifically, we study the influence of the matrix N and Θ1 which is the center of a restricted set to the admissibility of linear estimators in multivariate linear models with respect to the incomplete ellipsoidal restriction tr（Θ - Θ1）′N（Θ - Θ1） ≤σ^2. The main results show that the class of admissible linear estimators with the restriction tr（Θ - Θ1）′N（Θ - Θ1） ≤σ^2 is the same as the one with the restriction tr（Θ - Θ1）′N（Θ - Θ1） ≤σ^2 for Θ1 and Θ2 with certain relationship.

关 键 词：可容许性 不完全椭球约束 线性估计 多元线性模型 

分 类 号：O212[理学—概率论与数理统计]