Stability of the Ghurye-Olkin Characterization of Vector Gaussian Distributions
<|reference_start|>Stability of the Ghurye-Olkin Characterization of Vector Gaussian Distributions: 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 Cram\'er, respectively. The results are used to prove stability theorems for differential entropies of Gaussian vectors and blind source separation of non-Gaussian sources.<|reference_end|>
@article{mahvari2024stability,
    title={Stability of the Ghurye-Olkin Characterization of Vector Gaussian
  Distributions},
    author={Mahdi Mahvari and Gerhard Kramer},
    journal={arXiv preprint arXiv:2405.01707},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.01707},
    primaryClass={cs.IT math.IT}
}