An explicit Wishart moment formula for the product of two disjoint principal minors
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915182663434240 |
|---|---|
| author | Genest, Christian Ouimet, Frédéric Richards, Donald |
| author_facet | Genest, Christian Ouimet, Frédéric Richards, Donald |
| contents | This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks in 1934 in the Annals of Mathematics. The proof makes crucial use of hypergeometric functions of matrix argument and their Laplace transforms. Additionally, a Wishart generalization of the Gaussian product inequality conjecture is formulated and a stronger quantitative version is proved to hold in the case of two minors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit Wishart moment formula for the product of two disjoint principal minors Genest, Christian Ouimet, Frédéric Richards, Donald Probability Statistics Theory 60E05, 33C20, 39B62, 44A10, 60E15, 60G15 This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks in 1934 in the Annals of Mathematics. The proof makes crucial use of hypergeometric functions of matrix argument and their Laplace transforms. Additionally, a Wishart generalization of the Gaussian product inequality conjecture is formulated and a stronger quantitative version is proved to hold in the case of two minors. |
| title | An explicit Wishart moment formula for the product of two disjoint principal minors |
| topic | Probability Statistics Theory 60E05, 33C20, 39B62, 44A10, 60E15, 60G15 |
| url | https://arxiv.org/abs/2409.14512 |