IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v9y1979i4p511-530.html
   My bibliography  Save this article

Limit theorems for polylinear forms

Author

Listed:
  • Rotar', V. I.

Abstract

The limit theorems for polylinear forms are obtained. Conditions are found under which the distribution of the polylinear form of many random variables is essentially the same as if all the distributions of arguments were normal.

Suggested Citation

  • Rotar', V. I., 1979. "Limit theorems for polylinear forms," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 511-530, December.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:4:p:511-530
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(79)90055-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

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


    Cited by:

    1. Shuyang Bai & Murad S. Taqqu, 2016. "The Universality of Homogeneous Polynomial Forms and Critical Limits," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1710-1727, December.
    2. Yuta Koike, 2023. "High-Dimensional Central Limit Theorems for Homogeneous Sums," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-45, March.
    3. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    4. Peng, Hanxiang & Schick, Anton, 2018. "Asymptotic normality of quadratic forms with random vectors of increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 22-39.
    5. Youri Davydov & Vladimir Rotar, 2009. "On Asymptotic Proximity of Distributions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 82-98, March.
    6. Nourdin, Ivan & Poly, Guillaume, 2015. "An invariance principle under the total variation distance," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2190-2205.
    7. Bartels, Knut, 1998. "A model specification test," SFB 373 Discussion Papers 1998,109, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    8. Ivan Nourdin & Giovanni Peccati & Guillaume Poly & Rosaria Simone, 2016. "Classical and Free Fourth Moment Theorems: Universality and Thresholds," Journal of Theoretical Probability, Springer, vol. 29(2), pages 653-680, June.

    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:9:y:1979:i:4:p:511-530. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.