检验k母体协差阵相等中的不变性问题

<正> 设X′=(x_(1),…,x_(n)),x_(i):p×1,t=1,…,n.记n_i=n_1+…+n_i,n_i>p,n=n_1+…+n_k,x_(ni+1),…,x_(ni+ni+1)来自多元正态总体N_p(μ_i,∑_i),μ_i∈R~p,∑_i∈δ_p,容量为n_(i+1)的样本,i=1,…,k,其中δ_p={∑|∑:p×p,∑>0}.考虑     

矩阵椭球等高分布族

§1 引言 本文采用下速记号:指随机矩阵与具有相同的分布函数。O(n)为全体n×n正交阵之集合,对矩阵,写≥0(或>0)指是非负定阵(或正定阵),若>0,由线性代数的知识可知,存在唯一的一个正     

On The Spectral Decompositions of Spherical Matrix DistributionS and Some of Their Subclasses

In the viewpoint of spectral docomposition we study the spherical matrix distributions and obtain some new subclasses of Left-spherical distributions class.We also investigate rudely their properties and get some interesting examples.     

RELATIONSHIPS AMONG CLASSES OF SPHERICAL MATRIX DISTRIBUTIONS

Several classes of spherical matrix distributions have been studied by many authors.In thispaper the relationships among the classes are discussed in the following aspects:the characteristicfunctions in these classes,coordinate transformations,marginal distributions,marginal densities,and sphericity.Some statistics that are invariant in these classes are listed for applications.     

关于球阵分布及其某些子类的谱分解

In the viewpoint of spectral docomposition we study the spherical matrix distributions and obtain some new subclasses of Left-spherical distributions class. We also investigate rudely their properties and get some interesting examples.