成分数据统计分析中变异矩阵若干性质及应用

Some Properties of the Variation Matrix in the Statistical Analysis of Compositional Data and Some Applications

本文对成分数据统计分析中出现的变异矩阵 T、对数比协方差阵Σ及中心化对数比协方差阵Γ的秩、特征值等关系进行了讨论.证明了 T 非奇异时只有一个正特征值,还证明了此时 T 不可约.我们发现—T 是一个欧氏距离矩阵,并给出了一个统计应用.

The relationshipsh among the matrices T,Σ,Γ in the statistical analysis of compositional data are discussed in this paper.The facts that if det T≠0 then only one of theigenvalues of T is posi- tive,and T is an irreducible matrix are proved.Moreover T is an Euclidean distance matrix and its ap- piication is illustrated.