Projective Wishart Distributions
Statistics Theory
2024-07-16 v1 Probability
Statistics Theory
Abstract
We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the affine-invariant geometry of symmetric positive definite matrices in the real case or Hermitian positive definite matrices in the complex case. First, the Fr{\'e}chet mean of a projective Wishart distribution is the covariance parameter, up to a scaling factor, of the corresponding Wishart distribution. Second, in the case of 2 by 2 matrices, the densities have simple expressions in term of the affine-invariant distance.
Cite
@article{arxiv.2407.09582,
title = {Projective Wishart Distributions},
author = {Emmanuel Chevallier},
journal= {arXiv preprint arXiv:2407.09582},
year = {2024}
}