Moments for Left Elliptically Contoured Random Matrices

✍ Scribed by C.S. Wong; D. Liu

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 648 KB
• Volume: 49
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1994.1010

✦ Synopsis

For a left elliptically contoured (n \times p) random matrix (Y \sim \operatorname{LEC}{n \times p}(\mu, K, \phi)), the (m) th order moment (E\left(\otimes^{m} Y\right)) is obtained in terms of (\mu, K), and (\phi). When (K=B \otimes C), (\operatorname{LEC}{n \times p}(\mu, K, \phi)) is the conventional multivariate left elliptically contoured distribution MLEC ((\mu, A \otimes \Sigma, \phi)), where (A=B^{\prime} B) and (\Sigma=C^{\prime} C). Even if (Y \sim N_{n \times p}\left(\mu, \Sigma_{Y}\right)), the formula given here is new in that (\mu) need not be 0 and (\Sigma_{Y}) need not have the form (A \otimes \Sigma . \quad) : 1994 Academic Press, Inc