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Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix

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  • Takayama, Nobuki
  • Jiu, Lin
  • Kuriki, Satoshi
  • Zhang, Yi

Abstract

We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.

Suggested Citation

  • Takayama, Nobuki & Jiu, Lin & Kuriki, Satoshi & Zhang, Yi, 2020. "Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x20302232
    DOI: 10.1016/j.jmva.2020.104642
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    References listed on IDEAS

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    1. Takesi Hayakawa, 1969. "On the distribution of the latent roots of a positive definite random symmetric matrix I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 1-21, December.
    2. Hashiguchi, Hiroki & Numata, Yasuhide & Takayama, Nobuki & Takemura, Akimichi, 2013. "The holonomic gradient method for the distribution function of the largest root of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 296-312.
    3. Chiani, Marco, 2016. "Distribution of the largest root of a matrix for Roy’s test in multivariate analysis of variance," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 467-471.
    4. Krishnaiah, P. R. & Chang, T. C., 1971. "On the exact distributions of the extreme roots of the Wishart and MANOVA matrices," Journal of Multivariate Analysis, Elsevier, vol. 1(1), pages 108-117, April.
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    Cited by:

    1. Hideto Nakashima & Piotr Graczyk, 2022. "Wigner and Wishart ensembles for sparse Vinberg models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 399-433, June.

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