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arXiv · 2407.09582

Projective Wishart Distributions

Emmanuel Chevallier
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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.

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Emmanuel Chevallier. 2024-07-12. Projective Wishart Distributions. https://doi.org/10.1007/978-3-031-38271-0_44

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