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Bayesian joint-quantile regression

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Abstract

Estimation of low or high conditional quantiles is called for in many applications, but commonly encountered data sparsity at the tails of distributions makes this a challenging task. We develop a Bayesian joint-quantile regression method to borrow information across tail quantiles through a linear approximation of quantile coefficients. Motivated by a working likelihood linked to the asymmetric Laplace distributions, we propose a new Bayesian estimator for high quantiles by using a delayed rejection and adaptive Metropolis and Gibbs algorithm. We demonstrate through numerical studies that the proposed estimator is generally more stable and efficient than conventional methods for estimating tail quantiles, especially at small and modest sample sizes.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11631003, 11690012, 11726629 and 11701491), and Grant DMS-1712760 and the IR/D program from the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.

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Authors and Affiliations

  1. College of Mathematics and System Science, Xinjiang University, Urumqi, 830046, Xinjiang Uygur Autonomous Region, People’s Republic of China

    Yingying Hu

  2. Department of Statistics, The George Washington University, Washington, DC, 20052, USA

    Huixia Judy Wang

  3. Department of Statistics, University of Michigan, Ann Arbor, MI, 48109, USA

    Xuming He

  4. School of Mathematics and Statistics and KLAS, Northeast Normal University, Changchun, 130024, Jilin Province, People’s Republic of China

    Jianhua Guo

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  1. Yingying Hu
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  2. Huixia Judy Wang
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  3. Xuming He
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  4. Jianhua Guo
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Correspondence to Yingying Hu.

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Hu, Y., Wang, H.J., He, X. et al. Bayesian joint-quantile regression. Comput Stat 36, 2033–2053 (2021). https://doi.org/10.1007/s00180-020-00998-w

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