DOIAbstract
AbstractA d-dimensional positive definite correlation matrix R=(ρij) can be parametrized in terms of the correlations ρi,i+1 for i=1,…,d-1, and the partial correlations ρij|i+1,…j-1 for j-i⩾2. These d2 parameters can independently take values in the interval (-1,1). Hence we can generate a random positive definite correlation matrix by choosing independent distributions Fij, 1⩽i<j⩽d, for these d2 parameters. We obtain conditions on the Fij so that the joint density of (ρij) is proportional to a power of det(R) and hence independent of the order of indices defining the sequence of partial correlations. As a special case, we have a simple construction for generating R that is uniform over the space of positive definite correlation matrices. A...
Add to ORKG