The Beta-MANOVA Ensemble with General Covariance
We find the joint generalized singular value distribution and largest generalized singular value distributions of the β -MANOVA ensemble with positive diagonal covariance, which is general. This has been done for the continuous β > 0 case for identity covariance (in eigenvalue form), a...
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World Scientific Pub Co Pte Lt
2018
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| Online Access: | http://hdl.handle.net/1721.1/116005 https://orcid.org/0000-0001-7676-3133 |
| _version_ | 1811094809923813376 |
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| author | Dubbs, Alexander Joseph Edelman, Alan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Dubbs, Alexander Joseph Edelman, Alan |
| author_sort | Dubbs, Alexander Joseph |
| collection | MIT |
| description | We find the joint generalized singular value distribution and largest generalized singular value distributions of the β -MANOVA ensemble with positive diagonal covariance, which is general. This has been done for the continuous β > 0 case for identity covariance (in eigenvalue form), and by setting the covariance to I in our model we get another version. For the diagonal covariance case, it has only been done for β = 1, 2, 4 cases (real, complex, and quaternion matrix entries). This is in a way the first second-order β-ensemble, since the sampler for the generalized singular values of the β-MANOVA with diagonal covariance calls the sampler for the eigenvalues of the β-Wishart with diagonal covariance of Forrester and Dubbs-Edelman-Koev-Venkataramana. We use a conjecture of MacDonald proven by Baker and Forrester concerning an integral of a hypergeometric function and a theorem of Kaneko concerning an integral of Jack polynomials to derive our generalized singular value distributions. In addition we use many identities from Forrester’s Log-Gases and Random Matrices. We supply numerical evidence that our theorems are correct. |
| first_indexed | 2024-09-23T16:05:28Z |
| format | Article |
| id | mit-1721.1/116005 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:05:28Z |
| publishDate | 2018 |
| publisher | World Scientific Pub Co Pte Lt |
| record_format | dspace |
| spelling | mit-1721.1/1160052022-10-02T06:18:21Z The Beta-MANOVA Ensemble with General Covariance Dubbs, Alexander Joseph Edelman, Alan Massachusetts Institute of Technology. Department of Mathematics Dubbs, Alexander Joseph Edelman, Alan Finite random matrix theory; beta-ensembles; MANOVA We find the joint generalized singular value distribution and largest generalized singular value distributions of the β -MANOVA ensemble with positive diagonal covariance, which is general. This has been done for the continuous β > 0 case for identity covariance (in eigenvalue form), and by setting the covariance to I in our model we get another version. For the diagonal covariance case, it has only been done for β = 1, 2, 4 cases (real, complex, and quaternion matrix entries). This is in a way the first second-order β-ensemble, since the sampler for the generalized singular values of the β-MANOVA with diagonal covariance calls the sampler for the eigenvalues of the β-Wishart with diagonal covariance of Forrester and Dubbs-Edelman-Koev-Venkataramana. We use a conjecture of MacDonald proven by Baker and Forrester concerning an integral of a hypergeometric function and a theorem of Kaneko concerning an integral of Jack polynomials to derive our generalized singular value distributions. In addition we use many identities from Forrester’s Log-Gases and Random Matrices. We supply numerical evidence that our theorems are correct. 2018-05-31T12:13:31Z 2018-05-31T12:13:31Z 2014-01 2013-12 2018-05-21T12:48:59Z Article http://purl.org/eprint/type/JournalArticle 2010-3263 2010-3271 http://hdl.handle.net/1721.1/116005 DUBBS, ALEXANDER, and ALAN EDELMAN. “The Beta-MANOVA Ensemble with General Covariance." Random Matrices: Theory and Applications 03, no. 01 (January 2014): 1450002. https://orcid.org/0000-0001-7676-3133 http://dx.doi.org/10.1142/S2010326314500026 Random Matrices: Theory and Applications Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf World Scientific Pub Co Pte Lt arXiv |
| spellingShingle | Finite random matrix theory; beta-ensembles; MANOVA Dubbs, Alexander Joseph Edelman, Alan The Beta-MANOVA Ensemble with General Covariance |
| title | The Beta-MANOVA Ensemble with General Covariance |
| title_full | The Beta-MANOVA Ensemble with General Covariance |
| title_fullStr | The Beta-MANOVA Ensemble with General Covariance |
| title_full_unstemmed | The Beta-MANOVA Ensemble with General Covariance |
| title_short | The Beta-MANOVA Ensemble with General Covariance |
| title_sort | beta manova ensemble with general covariance |
| topic | Finite random matrix theory; beta-ensembles; MANOVA |
| url | http://hdl.handle.net/1721.1/116005 https://orcid.org/0000-0001-7676-3133 |
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