Star-shaped distributions and their generalizations
Statistics Theory
2008-08-17 v1 Statistics Theory
Abstract
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to ``star-shaped distributions'' with concentric star-shaped contours and show that many results in the former case continue to hold in the more general case. We develop a general theory in the framework of abstract group invariance so that the results can be applied to other cases as well, especially those involving random matrices.
Cite
@article{arxiv.math/0605600,
title = {Star-shaped distributions and their generalizations},
author = {Hidehiko Kamiya and Akimichi Takemura and Satoshi Kuriki},
journal= {arXiv preprint arXiv:math/0605600},
year = {2008}
}