IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v41y2014i8p1746-1766.html
   My bibliography  Save this article

Inference in multivariate linear regression models with elliptically distributed errors

Author

Listed:
  • M. Qamarul Islam
  • Fetih Yildirim
  • Mehmet Yazici

Abstract

In this study we investigate the problem of estimation and testing of hypotheses in multivariate linear regression models when the errors involved are assumed to be non-normally distributed. We consider the class of heavy-tailed distributions for this purpose. Although our method is applicable for any distribution in this class, we take the multivariate t -distribution for illustration. This distribution has applications in many fields of applied research such as Economics, Business, and Finance. For estimation purpose, we use the modified maximum likelihood method in order to get the so-called modified maximum likelihood estimates that are obtained in a closed form. We show that these estimates are substantially more efficient than least-square estimates. They are also found to be robust to reasonable deviations from the assumed distribution and also many data anomalies such as the presence of outliers in the sample, etc. We further provide test statistics for testing the relevant hypothesis regarding the regression coefficients.

Suggested Citation

  • M. Qamarul Islam & Fetih Yildirim & Mehmet Yazici, 2014. "Inference in multivariate linear regression models with elliptically distributed errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1746-1766, August.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:8:p:1746-1766
    DOI: 10.1080/02664763.2014.890177
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2014.890177
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2014.890177?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. Tiku, Moti L. & Islam, M. Qamarul & Sazak, Hakan S., 2008. "Estimation in bivariate nonnormal distributions with stochastic variance functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1728-1745, January.
    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. Graciliano M. S. Louredo & Camila B. Zeller & Clécio S. Ferreira, 2022. "Estimation and Influence Diagnostics for the Multivariate Linear Regression Models with Skew Scale Mixtures of Normal Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 204-242, May.

    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. Tiku, Moti L. & Senoglu, Birdal, 2009. "Estimation and hypothesis testing in BIB design and robustness," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3439-3451, July.
    2. M. Qamarul Islam & Moti Tiku, 2010. "Multiple linear regression model with stochastic design variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 923-943.
    3. Ping Chen & Jinde Wang, 2010. "Application in stochastic volatility models of nonlinear regression with stochastic design," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(2), pages 142-156, March.
    4. Tiku, Moti L. & Sürücü, Baris, 2009. "MMLEs are as good as M-estimators or better," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 984-989, April.
    5. Pelin Kasap & Birdal Senoglu & Olcay Arslan, 2016. "Stochastic analysis of covariance when the error distribution is long-tailed symmetric," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 1977-1997, August.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:41:y:2014:i:8:p:1746-1766. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.