多维正态分布协方差阵在环序和伞序约束下的极大似然估计
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摘要
通过对多维正态分布协方差阵采用参数化,利用在简单树半序和简单半序约束下协方差阵极大似然估计的方法,给出了多维正态分布协方差阵在简单环半序和伞型半序约束下极大似然估计的充分条件以及极大似然估计的计算方法,并给出多元平衡三向分类随机模型的应用实例.
According to the algorithm of maximum likelihood estimators of covariance matrices of multivariate normal distribution under simple tree ordering and simple ordering by parameterization technique for covariance matrices,sufficient condition and a new algorithm of maximum likelihood estimators of covariance matrices of multivariate normal distribution under simple ring ordering and umbrella ordering are proposed.The example of the completely balanced multivariate three-way random effects model without interaction is given.
According to the algorithm of maximum likelihood estimators of covariance matrices of multivariate normal distribution under simple tree ordering and simple ordering by parameterization technique for covariance matrices,sufficient condition and a new algorithm of maximum likelihood estimators of covariance matrices of multivariate normal distribution under simple ring ordering and umbrella ordering are proposed.The example of the completely balanced multivariate three-way random effects model without interaction is given.
引文
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[3]TSAI M T.Maximum likelihood estimation of covariance matrices under simple tree ordering[J].Journal of Multivariate Analysis,2004,89:292-303.
[4]TSAI M T.Maximum likelihood estimation of Wishart mean matrices under L9wner order restrictions[J].Journal of Multivariate Analysis,2007,98:932-944.
[5]MUIRHEAD R J.Aspects of multivariate statistical theory[M].New York:Wiley,1982:586-593.
[6]ROBERTSON T,WRIGHT F T,DYKSTRA R L.Order restricted statistical inference[M].New York:Wiley,1988:1-57.
[7]刘金山.Wishart分布引论[M].北京:科学出版社,2005:70-106.
[8]辛益军.方差分析与实验设计[M].北京:中国财政经济出版社,2001:150-176.
[2]CALVIN J A,DYKSTRA R L.Maximum likelihood estimation of a set of covariance matrices under L9wner order restrictions with applications to balanced multivariate variance components models[J].Ann Statist,1991,19:850-869.
[3]TSAI M T.Maximum likelihood estimation of covariance matrices under simple tree ordering[J].Journal of Multivariate Analysis,2004,89:292-303.
[4]TSAI M T.Maximum likelihood estimation of Wishart mean matrices under L9wner order restrictions[J].Journal of Multivariate Analysis,2007,98:932-944.
[5]MUIRHEAD R J.Aspects of multivariate statistical theory[M].New York:Wiley,1982:586-593.
[6]ROBERTSON T,WRIGHT F T,DYKSTRA R L.Order restricted statistical inference[M].New York:Wiley,1988:1-57.
[7]刘金山.Wishart分布引论[M].北京:科学出版社,2005:70-106.
[8]辛益军.方差分析与实验设计[M].北京:中国财政经济出版社,2001:150-176.