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Bayesian joint inference for multivariate quantile regression model with L $$_{1/2}$$ 1 / 2 penalty

Author

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  • Yu-Zhu Tian

    (Northwest Normal University)

  • Man-Lai Tang

    (The Hang Seng University of Hong Kong)

  • Mao-Zai Tian

    (Renmin University of China)

Abstract

This paper considers a Bayesian approach for joint estimation of the marginal conditional quantiles from several dependent variables under a linear regression framework. This approach incorporates the dependence among different dependent variables in the regression model which studies how the relationship between dependent variables and a set of explanatory variables can vary across different quantiles of the marginal conditional distribution of the dependent variables. A Bayesian regularization approach with L $$_{1/2}$$ 1 / 2 penalty is adopted to conduct high-dimensional variable selection. Some simulation studies are conducted to evaluate the performance of our proposed method. We illustrate the proposed estimation approach using a real data set on energy efficiency with two responses.

Suggested Citation

  • Yu-Zhu Tian & Man-Lai Tang & Mao-Zai Tian, 2021. "Bayesian joint inference for multivariate quantile regression model with L $$_{1/2}$$ 1 / 2 penalty," Computational Statistics, Springer, vol. 36(4), pages 2967-2994, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01158-4
    DOI: 10.1007/s00180-021-01158-4
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    References listed on IDEAS

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