IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v179y2020ics0047259x20302232.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X20302232
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2020.104642?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chételat, Didier & Narayanan, Rajendran & Wells, Martin T., 2018. "On the domain of attraction of a Tracy–Widom law with applications to testing multiple largest roots," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 132-142.
    2. Hashiguchi, Hiroki & Takayama, Nobuki & Takemura, Akimichi, 2018. "Distribution of the ratio of two Wishart matrices and cumulative probability evaluation by the holonomic gradient method," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 270-278.
    3. Tamio Koyama & Hiromasa Nakayama & Kenta Nishiyama & Nobuki Takayama, 2014. "Holonomic gradient descent for the Fisher–Bingham distribution on the $$d$$ d -dimensional sphere," Computational Statistics, Springer, vol. 29(3), pages 661-683, June.
    4. Aurelia Rybak & Aleksandra Rybak & Jarosław Joostberens, 2023. "The Impact of Removing Coal from Poland’s Energy Mix on Selected Aspects of the Country’s Energy Security," Sustainability, MDPI, vol. 15(4), pages 1-13, February.
    5. Bai, Zhidong & Silverstein, Jack W., 2022. "A tribute to P.R. Krishnaiah," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Daya K. Nagar & Raúl Alejandro Morán-Vásquez & Arjun K. Gupta, 2015. "Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-15, January.
    7. Armine Bagyan & Donald Richards, 2023. "Hoffmann-Jørgensen Inequalities for Random Walks on the Cone of Positive Definite Matrices," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1181-1202, June.
    8. Dharmawansa, Prathapasinghe & Nadler, Boaz & Shwartz, Ofer, 2019. "Roy’s largest root under rank-one perturbations: The complex valued case and applications," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    9. Shimizu, Koki & Hashiguchi, Hiroki, 2021. "Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:179:y:2020:i:c:s0047259x20302232. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.