A method for generating realistic correlation matrices

Details A method for generating realistic correlation matrices A method for generating realistic correlation matrices

2011-06-29

arxiv.org/abs/1106.5834v1

Mathematics

Statistics Theory

25 pages

Scientific paper

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating normal data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating normal data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Finally, using our results with an existing clustering algorithm, we show that simulating correlation matrices can help assess statistical methodology.

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