The class of distributions on $R^m, 1 \leq m < \infty$ which are the $m$-dimensional marginal distributions of orthogonally invariant distributions on $R^{m + n}$ is characterized. This result is then used to provide a partial answer to the following question: given a symmetric distribution on $R^1$ and an integer $n \geq 2$, under what conditions will there exist a random vector $X \in R^n$ such that $a'X$ has the given distribution (up to a positive scale factor) for all $a \neq 0, a \in R^m$.
Publié le : 1981-03-14
Classification:
$n$-dimensional distributions,
scale mixtures of normals,
orthogonally invariant distributions,
60E05,
62E10,
62H05
@article{1176345404,
author = {Eaton, Morris L.},
title = {On the Projections of Isotropic Distributions},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 391-400},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345404}
}
Eaton, Morris L. On the Projections of Isotropic Distributions. Ann. Statist., Tome 9 (1981) no. 1, pp. 391-400. http://gdmltest.u-ga.fr/item/1176345404/