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Robust Bayesian seemingly unrelated regression model

Author

Listed:
  • Chamberlain Mbah

    (Ghent University)

  • Kris Peremans

    (KU Leuven)

  • Stefan Van Aelst

    (KU Leuven)

  • Dries F. Benoit

    () (Ghent University)

Abstract

Abstract A robust Bayesian model for seemingly unrelated regression is proposed. By using heavy-tailed distributions for the likelihood, robustness in the response variable is attained. In addition, this robust procedure is combined with a diagnostic approach to identify observations that are far from the bulk of the data in the multivariate space spanned by all variables. The most distant observations are downweighted to reduce the effect of leverage points. The resulting robust Bayesian model can be interpreted as a heteroscedastic seemingly unrelated regression model. Robust Bayesian estimates are obtained by a Markov Chain Monte Carlo approach. Complications by using a heavy-tailed error distribution are resolved efficiently by representing these distributions as a scale mixture of normal distributions. Monte Carlo simulation experiments confirm that the proposed model outperforms its traditional Bayesian counterpart when the data are contaminated in the response and/or the input variables. The method is demonstrated on a real dataset.

Suggested Citation

  • Chamberlain Mbah & Kris Peremans & Stefan Van Aelst & Dries F. Benoit, 2019. "Robust Bayesian seemingly unrelated regression model," Computational Statistics, Springer, vol. 34(3), pages 1135-1157, September.
  • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-018-0854-3
    DOI: 10.1007/s00180-018-0854-3
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