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.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS638 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
