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Inference in multivariate linear regression models with elliptically distributed errors

Author

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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