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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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    Cited by:

    1. Kai Yang & Luan Zhao & Qian Hu & Wenshan Wang, 2024. "Bayesian Quantile Regression Analysis for Bivariate Vector Autoregressive Models with an Application to Financial Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 64(4), pages 1939-1963, October.
    2. Iacopini, Matteo & Poon, Aubrey & Rossini, Luca & Zhu, Dan, 2023. "Bayesian mixed-frequency quantile vector autoregression: Eliciting tail risks of monthly US GDP," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    3. YuZhu Tian & ChunHo Wu & ManLai Tang & MaoZai Tian, 2025. "Bayesian joint relatively quantile regression of latent ordinal multivariate linear models with application to multirater agreement analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(1), pages 85-116, March.

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