**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 1, pp. 115--125

**MOMENTS FOR ELLIPTICALLY CONTOURED RANDOM MATRICES II**

By

TONGHUI WANG, *New Mexico State University*

SUMMARY. For an elliptically contoured n x p random matrix $Y ~ MEC_{n \times p}(\mu, \sum_{Y}, \phi)$, the higher order moments of both Y and its quadratic forms are obtained in terms of $\mu$, $\sum_{Y}$ and $\phi$. These formulae are general in that Y need not be normal and $\sum_{Y}$ is no longer required to have the form $A\otimes\sum$. Among others, these results are applied to the multivariate components of the variance model $MEC_{n \times p}(\mu, \sum_{Y}, \phi)$ with $\sum_{Y}= \sum_{j=1}^{k}V_{j}\otimes \sum_{j}$.

*AMS (1980) subject classification.* Primary 62H0J, secondary 62H99.

*Key words and phrases.* Characteristic function, higher order moments, second degree matrix polynomial, multivariate components of variance model, symmetric multivariate Pearson Type VII distribution, trace inner product.