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On the condensed density of the generalized eigenvalues of pencils of Gaussian random matrices and applications

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  • Barone, Piero

Abstract

Pencils of matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which allows to get a closed form approximation of the condensed density of the generalized eigenvalues of the pencils. Implications of this result for solving several moments problems are discussed and some numerical examples are provided.

Suggested Citation

  • Barone, Piero, 2012. "On the condensed density of the generalized eigenvalues of pencils of Gaussian random matrices and applications," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 160-173.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:160-173
    DOI: 10.1016/j.jmva.2012.05.009
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    References listed on IDEAS

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    1. Barone, P., 2011. "A generalization of Bartlett's decomposition," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 371-381, March.
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    Cited by:

    1. Barone, P., 2013. "On the condensed density of the zeros of the Cauchy transform of a complex atomic random measure with Gaussian moments," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2569-2576.
    2. Barone, P., 2016. "Bivariate one-sample optimal location test for spherical stable densities by Pade’ methods," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 189-199.

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    1. Barone, P., 2013. "On the condensed density of the zeros of the Cauchy transform of a complex atomic random measure with Gaussian moments," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2569-2576.

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