pqrBayes: Bayesian Penalized Quantile Regression

Bayesian regularized quantile regression utilizing two major classes of shrinkage priors (the spike-and-slab priors and the horseshoe family of priors) leads to efficient Bayesian shrinkage estimation, variable selection and valid statistical inference. In this package, we have implemented robust Bayesian variable selection with spike-and-slab priors under high-dimensional linear regression models (Fan et al. (2024) <doi:10.3390/e26090794> and Ren et al. (2023) <doi:10.1111/biom.13670>), and regularized quantile varying coefficient models (Zhou et al.(2023) <doi:10.1016/j.csda.2023.107808>). In particular, valid robust Bayesian inferences under both models in the presence of heavy-tailed errors can be validated on finite samples. Additional models with spike-and-slab priors include robust Bayesian group LASSO and robust binary Bayesian LASSO (Fan and Wu (2025) <doi:10.1002/sta4.70078>). Besides, robust sparse Bayesian regression with the horseshoe family of (horseshoe, horseshoe+ and regularized horseshoe) priors has also been implemented and yielded valid inference results under heavy-tailed model errors (Fan et al.(2026) <doi:10.1016/j.csda.2026.108358>). The Markov chain Monte Carlo (MCMC) algorithms of the proposed and alternative models are implemented in C++.

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