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

✍ Scribed by Dorota Kurowicka; Roger Cooke

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 221 KB
• Volume: 372
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00507-x

✦ Synopsis

We present a parameterization of the class PD(n) of positive definite n × n matrices using regular vines and partial correlations. Using a bijection from (-1, 1)

is the class of n × 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.