摘要
混合效应模型是统计模型中非常重要的一类模型,广泛地应用到许多领域.本文比较了该模型下方差分量的两种估计:方差分析(ANOVA)估计和谱分解(SD)估计,借助吴密霞和王松桂[A new method of spectral decomposition of covariance matrix in mixed effects models and its applications,Sci.China,Ser.A,2005,48:1451-1464]协方差矩阵的谱分解结果,给出了ANOVA估计和SD估计相等的两个充分条件及其相应的统计性质,并将以上的结果应用于圆形部件数据模型和混合方差分析模型.
The mixed-effects models are an important class of statistical models that are used in many fields of applications.For these models,we compare two estimators of the variance components,the analysis of variance(ANOVA) estimator and the spectral decomposition(SD) estimator.Based on the spectral decomposition of covariance matrix[A new method of spectral decomposition of covariance matrix in mixed effects models and its applications,Sci.China,Ser.A,2005,48:1451-1464],we establish two sufficient conditions for the identity of ANOVA estimator and SD estimator,and present some corresponding statistical properties of ANOVA estimator and SD estimator.Applications of the methods to circular models and mixed analysis of variance models are discussed.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2014年第3期615-624,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(11171011
11001012)
北京市自然科学基金(1132007)
北京市属高等学校人才强教深化计划(中青年骨干人才培养计划RHR20110820)
北京工业大学京华人才培养计划
关键词
方差分析
谱分解
混合效应模型
analysis of variance
spectral decomposition
mixed-effects model
