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...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.展开更多
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 th...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.展开更多
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).
文摘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.
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
文摘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.
