A new method for generating random correlation matrices

Abstract

Summary We propose a new method for generating random correlation matrices that makes it simple to control both location and dispersion. The method is based on a vector parameterization, $\gamma =g(C)$, which maps any distribution on $\mathbb {R}^{n(n-1)/2}$ to a distribution on the space of nonsingular $n\times n$ correlation matrices. Correlation matrices with certain properties, such as being well-conditioned, having block structures, and having strictly positive elements, are simple to generate. We compare the new method with existing methods.