Bayesian joint-quantile regression

Yingying Hu (), Huixia Judy Wang (), Xuming He () and Jianhua Guo ()
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Yingying Hu: Xinjiang University
Huixia Judy Wang: The George Washington University
Xuming He: University of Michigan
Jianhua Guo: Northeast Normal University

Computational Statistics, 2021, vol. 36, issue 3, No 23, 2033-2053

Abstract: 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.

Keywords: Adaptive Metropolis; Asymmetric Laplace distribution; Delayed rejection; High quantile; Quantile regression (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-00998-w

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