Simultaneous optimal estimates of fixed effects and variance components in the mixed model

作     者：WU Mixia WANG Songgui 

作者机构：College of Applied Sciences Beijing University of Technology Beijing 100022 College of Applied Sciences Beijing University of Technology Beijing 100022 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2004年第47卷第5期

页      面：787-799页

核心收录：

学科分类：07[理学] 08[工学] 

基　　金：This work was partially supported by the National Natural Science Foundation of China(Grant No.10271010) the Natural Science Foundation of Beijing(Grant Mo.1032001) 

主　　题：linear mixed model, random effect, variance component, minimum variance unbiased estimate,uniformly most powerful unbiased test. 

摘      要：For a general linear mixed model with two variance components, a set of simple conditions is obtained, under which, (i) the least squares estimate of the fixed effects and the analysis of variance (ANOVA) estimates of variance components are proved to be uniformly minimum variance unbiased estimates simultaneously; (ii) the exact confidence intervals of the fixed effects and uniformly optimal unbiased tests on variance components are given; (iii) the exact probability expression of ANOVA estimates of variance components taking negative value is obtained.