Volume no :19, Issue no: 2, June (2018)

Journal of Statistics: Advances in Theory and Applications

EXACT DISTRIBUTION OF THE LARGEST AND SMALLEST EIGENVALUES OF THE RATIO OF TWO ELLIPTICAL WISHART MATRICES

Author's: Aya Shinozaki and Hiroki Hashiguchi
Pages: [71] - [82]
Received Date: June 30, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121983

Abstract

We discuss a class of generalized Wishart distributions under elliptical models that is called the elliptical Wishart distribution. We derive the distribution of the largest and smallest eigenvalues for the ratio of two sample Wishart matrices under elliptical models. These general results include classical expressions for the Gaussian model. We also discuss a matrix-variate t distribution as a special case.

Keywords

eigenvalue distribution, elliptically contoured distribution, matrix-variate, zonal polynomial.