Simultaneous Optimality of LSE and ANOVA Estimate in General Mixed Models  

作　　者：Mi Xia WU Song Gui WANG Kai Fun YU 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100022, P. R. China [2]Division of Epidemiology, Statistics and Prevention Research, National Institute of Child Health and Human Development,NIHJDHHS, 6100 Executive Boulevard, RockviUe, MD 20852, USA [3]Division of Epidemiology, Statistics and Prevention Research, National Institute of Child Health and Human Development,NIH/DHHS, 6100 Executive Boulevard, Rockville, MD 20852, USA

出　　处：《Acta Mathematica Sinica,English Series》2008年第10期1637-1650,共14页数学学报（英文版）

基　　金：Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality PHR (IHLB);National Natural Science Foundation of China (NSFC) (10801005) and (NSFC) (10771010);the Intramural Research Program of the National Institute of Child Health and Human Development,National Institute of Health

摘　　要：Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance （Hendreson III＇s） estimate of variance components being uniformly minimum variance unbiased estimates simultaneously. This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest, and for finding equivalences of several common estimates of variance components.Problems of the simultaneous optimal estimates and the optimal tests in general mixed models are considered. A necessary and sufficient condition is presented for the least squares estimate of the fixed effects and the analysis of variance （Hendreson III＇s） estimate of variance components being uniformly minimum variance unbiased estimates simultaneously. This result can be applied to the problems of finding uniformly optimal unbiased tests and uniformly most accurate unbiased confidential interval on parameters of interest, and for finding equivalences of several common estimates of variance components.

关 键 词：Linear mixed model Least squares estimate Analysis of variance estimate Minimum variance unbiased estimate Uniformly most powerful unbiased test 

分 类 号：O15[理学—数学]