Generation of correlation matrices with a given eigen–structure
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A Priori information on the nature of the components of a random vector often leads one to examine associations between subsets of these components. However one is often uncertain as to whether the observed associations could have been obtained for quite arbitrary sub-sets due to some inherent overall structure in the data. Such structure is usually revealed by the eigen-values of the variance-covariance or correlation matrix of the variables. This paper presents an algorithm which enables one to investigate empirically such induced dependence by generating a large number of correlation matrices with identical eigen-values to those observed.