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.

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This article in Mathematical Reviews.