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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.01707 |
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| _version_ | 1866914073482887168 |
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| author | Mahvari, Mahdi Kramer, Gerhard |
| author_facet | Mahvari, Mahdi Kramer, Gerhard |
| contents | The stability of the Ghurye-Olkin (GO) characterization of Gaussian vectors is analyzed using a partition of the vectors into equivalence classes defined by their matrix factors. The sum of the vectors in each class is near-Gaussian in the characteristic function (c.f.) domain if the GO independence condition is approximately met in the c.f. domain. All vectors have the property that any vector projection is near-Gaussian in the distribution function (d.f.) domain. The proofs of these c.f. and d.f. stabilities use tools that establish the stabilities of theorems by Kac-Bernstein and Cramér, respectively. The results are used to prove stability theorems for differential entropies of Gaussian vectors and blind source separation of non-Gaussian sources. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of the Ghurye-Olkin Characterization of Vector Gaussian Distributions Mahvari, Mahdi Kramer, Gerhard Information Theory The stability of the Ghurye-Olkin (GO) characterization of Gaussian vectors is analyzed using a partition of the vectors into equivalence classes defined by their matrix factors. The sum of the vectors in each class is near-Gaussian in the characteristic function (c.f.) domain if the GO independence condition is approximately met in the c.f. domain. All vectors have the property that any vector projection is near-Gaussian in the distribution function (d.f.) domain. The proofs of these c.f. and d.f. stabilities use tools that establish the stabilities of theorems by Kac-Bernstein and Cramér, respectively. The results are used to prove stability theorems for differential entropies of Gaussian vectors and blind source separation of non-Gaussian sources. |
| title | Stability of the Ghurye-Olkin Characterization of Vector Gaussian Distributions |
| topic | Information Theory |
| url | https://arxiv.org/abs/2405.01707 |