TESTS OF SIGNIFICANCE IN MULTIVARIATE ANALYSIS
TESTS OF SIGNIFICANCE IN MULTIVARIATE ANALYSIS
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DOI：
10.2307/2332629
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发表时间：
1948-01-01
期刊：
影响因子：
2.7
通讯作者：
RAO, CR
中科院分区：
文献类型：
--
作者：
RAO, CR
一个统一的方法来解决这个问题，利用的概念，类似的方差分析的单变量的情况下，分散。给出方差和协方差的无偏估计的均值乘积矩阵称为误差矩阵;仅在零假设下才产生无偏估计的均值乘积矩阵称为误差矩阵，该矩阵是由于偏离假设而产生的。的approp。检验准则是行列式方程的根。Wilk的A准则与根的集合有关。当去掉由另一组变量引起的离差时，分析一组变量的离差的问题也依赖于A。一些例子说明计算过程包括在内。
A unified approach to the problem is given, making use of the concept of analysis of dispersion in analogy with the analysis of variance for the univariate case. The matrix of mean products giving unbiased estimates of the variances and covariances is called the error matrix; that of mean products yielding unbiased estimates only under the null hypothesis, the matrix due to deviation from the hypothesis. The approp. test criterion is a root of a determinantal equation. Wilk''s A criterion is related to the set of roots. The problem of analysis of dispersion of 1 set of variables when the dispersion due to another set is removed is shown to depend also on A. A number of examples illustrating computational procedure are included.