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September 2013 A method for generating realistic correlation matrices
Johanna Hardin, Stephan Ramon Garcia, David Golan
Ann. Appl. Stat. 7(3): 1733-1762 (September 2013). DOI: 10.1214/13-AOAS638


Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian 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 Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices can help assess statistical methodology.


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Johanna Hardin. Stephan Ramon Garcia. David Golan. "A method for generating realistic correlation matrices." Ann. Appl. Stat. 7 (3) 1733 - 1762, September 2013.


Published: September 2013
First available in Project Euclid: 3 October 2013

zbMATH: 06237195
MathSciNet: MR3127966
Digital Object Identifier: 10.1214/13-AOAS638

Keywords: Correlation matrix , Eigenvalues , simulating matrices , Toeplitz matrix , Weyl inequalities

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.7 • No. 3 • September 2013
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