On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929443551838208 |
|---|---|
| author | Genest, Christian Ouimet, Frédéric Richards, Donald |
| author_facet | Genest, Christian Ouimet, Frédéric Richards, Donald |
| contents | In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample statistics in various applications related to multivariate linear regression. These important but little-known moment results were extended in 1963 by the Australian statistician A. Graham Constantine using Bartlett's decomposition. In this note, a new proof of Wilks' results is derived using the concept of iterated Schur complements, thereby bypassing Bartlett's decomposition. Furthermore, Wilks' open problem of evaluating joint moments of disjoint principal minors of Wishart random matrices is related to the Gaussian product inequality conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06330 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices Genest, Christian Ouimet, Frédéric Richards, Donald Statistics Theory Probability 62E15, 60E15, 62H10, 62H12 In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample statistics in various applications related to multivariate linear regression. These important but little-known moment results were extended in 1963 by the Australian statistician A. Graham Constantine using Bartlett's decomposition. In this note, a new proof of Wilks' results is derived using the concept of iterated Schur complements, thereby bypassing Bartlett's decomposition. Furthermore, Wilks' open problem of evaluating joint moments of disjoint principal minors of Wishart random matrices is related to the Gaussian product inequality conjecture. |
| title | On Wilks' joint moment formulas for embedded principal minors of Wishart random matrices |
| topic | Statistics Theory Probability 62E15, 60E15, 62H10, 62H12 |
| url | https://arxiv.org/abs/2403.06330 |