Projective Wishart Distributions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917721473548288 |
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| author | Chevallier, Emmanuel |
| author_facet | Chevallier, Emmanuel |
| contents | 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{é}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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective Wishart Distributions Chevallier, Emmanuel Statistics Theory Probability 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{é}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. |
| title | Projective Wishart Distributions |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2407.09582 |