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Matrix-variate distribution theory under elliptical models-4: Joint distribution of latent roots of covariance matrix and the largest and smallest latent roots

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  • Caro-Lopera, Francisco J.
  • González Farías, Graciela
  • Balakrishnan, Narayanaswamy

Abstract

In this work, we derive the joint distribution of the latent roots of a sample covariance matrix under elliptical models. We then obtain the distributions of the largest and smallest latent roots. In the process of these derivations, we also correct some results present in the literature.

Suggested Citation

  • Caro-Lopera, Francisco J. & González Farías, Graciela & Balakrishnan, Narayanaswamy, 2016. "Matrix-variate distribution theory under elliptical models-4: Joint distribution of latent roots of covariance matrix and the largest and smallest latent roots," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 224-235.
    • Handle: RePEc:eee:jmvana:v:145:y:2016:i:c:p:224-235
    DOI: 10.1016/j.jmva.2015.12.012
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    References listed on IDEAS

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    1. Khatri, C. G., 1972. "On the exact finite series distribution of the smallest or the largest root of matrices in three situations," Journal of Multivariate Analysis, Elsevier, vol. 2(2), pages 201-207, June.
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    Cited by:

    1. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 323-345, June.

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