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The emperor's new clothes: a critique of the multivariate t regression model

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  • T. S. Breusch
  • J. C. Robertson
  • A. H. Welsh

Abstract

Zellner (1976) proposed a regression model in which the data vector (or the error vector) is represented as a realization from the multivariate Student t distribution. This model has attracted considerable attention because it seems to broaden the usual Gaussian assumption to allow for heavier‐tailed error distributions. A number of results in the literature indicate that the standard inference procedures for the Gaussian model remain appropriate under the broader distributional assumption, leading to claims of robustness of the standard methods. We show that, although mathematically the two models are different, for purposes of statistical inference they are indistinguishable. The empirical implications of the multivariate t model are precisely the same as those of the Gaussian model. Hence the suggestion of a broader distributional representation of the data is spurious, and the claims of robustness are misleading. These conclusions are reached from both frequentist and Bayesian perspectives.

Suggested Citation

  • T. S. Breusch & J. C. Robertson & A. H. Welsh, 1997. "The emperor's new clothes: a critique of the multivariate t regression model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(3), pages 269-286, November.
  • Handle: RePEc:bla:stanee:v:51:y:1997:i:3:p:269-286
    DOI: 10.1111/1467-9574.00055
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    Cited by:

    1. Enzo D’Innocenzo & Alessandra Luati & Mario Mazzocchi, 2023. "A robust score-driven filter for multivariate time series," Econometric Reviews, Taylor & Francis Journals, vol. 42(5), pages 441-470, May.
    2. Reinaldo Arellano-Valle & Marc Genton, 2010. "An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 363-381, April.
    3. Shuangzhe Liu & Chris Heyde, 2008. "On estimation in conditional heteroskedastic time series models under non-normal distributions," Statistical Papers, Springer, vol. 49(3), pages 455-469, July.
    4. Castilla, Elena & Zografos, Konstantinos, 2022. "On distance-type Gaussian estimation," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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