A parameterization of positive definite matrices in terms of partial correlation vines

摘要

We present a parameterization of the class PD(n) of positive definite n x n matrices using regular vines and partial correlations. Using a bijection from (-1,1)(()(n))(2) --> C(n) (C(n) is the class of n x n correlation matrices) with a clear probabilistic interpretation [Ann. Statist. 30 (4) (2002) 1031], we suggest a new approach to various problems involving positive definiteness. (C) 2003 Elsevier Inc. All rights reserved. [References: 10]