A novel Bayesian computational approach for bridge-randomized quantile regression in high dimensional models

References

• Koenker R, Bassett G. Regression quantiles. Econometrica. 1978;46:33–50. doi: 10.2307/1913643
   Web of Science ®Google Scholar
• Koenker R, Park BJ. An interior point algorithm for nonlinear quantile regression. J Econom. 1996;71:265–283. doi: 10.1016/0304-4076(96)84507-6
   Web of Science ®Google Scholar
• Hunter DR, Lange K. Quantile regression via an MM algorithm. J Comput Graph Stat. 2000;9:60–77. doi: 10.1080/10618600.2000.10474866
   Web of Science ®Google Scholar
• Tian Y, Tian M, Zhu Q. Linear quantile regression based on EM algorithm. Commun Stat – Theory Methods. 2014;43:3464–3484. doi: 10.1080/03610926.2013.766339
   Web of Science ®Google Scholar
• Yu K, Moyeed RA. Bayesian quantile regression. Stat Probab Lett. 2001;54:437–447. doi: 10.1016/S0167-7152(01)00124-9
   Web of Science ®Google Scholar
• Koenker R. Quantile regression for longitudinal data. J Multivar Anal. 2004;91:74–89. doi: 10.1016/j.jmva.2004.05.006
   Web of Science ®Google Scholar
• Li Y, Zhu J. l1-norm quantile regression. J Comput Graph Stat. 2008;17:163–185. doi: 10.1198/106186008X289155
   Web of Science ®Google Scholar
• Wang H, Li G, Jiang G. Robust regression shrinkage and consistent variable selection through the lad-lasso. J Bus Econ Stat. 2007;25:347–355. doi: 10.1198/073500106000000251
   Web of Science ®Google Scholar
• Wu Y, Liu Y. Variable selection in quantile regression. Stat Sin. 2009;19:801–817.
   Web of Science ®Google Scholar
• Mallick H, Alhamzawi R, Paul E, et al. The reciprocal Bayesian lasso. Stat Med. 2021;40:4830–4849. doi: 10.1002/sim.v40.22
   PubMed Web of Science ®Google Scholar
• Park T, Casella G. The Bayesian lasso. J Am Stat Assoc. 2008;103:681–686. doi: 10.1198/016214508000000337
   Web of Science ®Google Scholar
• Alhamzawi R, Ali HTM. Bayesian Tobit quantile regression with penalty. Commun Stat – Simul Comput. 2018;47:1739–1750. doi: 10.1080/03610918.2017.1323224
   Web of Science ®Google Scholar
• Alhamzawi R, Yu K, Benoit DF. Bayesian adaptive lasso quantile regression. Stat Modelling. 2012;12:279–297. doi: 10.1177/1471082X1101200304
   Web of Science ®Google Scholar
• Feng X-N, Wang Y, Lu B, et al. Bayesian regularized quantile structural equation models. J Multivar Anal. 2017;154:234–248. doi: 10.1016/j.jmva.2016.11.002
   Web of Science ®Google Scholar
• Li Q, Xi R, Lin N. Bayesian regularized quantile regression. Bayesian Anal. 2010;5:533–556.
   Web of Science ®Google Scholar
• Tian Y, Song X. Bayesian bridge-randomized penalized quantile regression. Comput Stat Data Anal. 2020;144:Article ID 106876. doi: 10.1016/j.csda.2019.106876
   Web of Science ®Google Scholar
• Tian Y, Song X. Fully Bayesian l1/2-penalized linear quantile regression analysis with autoregressive errors. Stat Interface. 2020;13:271–286. doi: 10.4310/SII.2020.v13.n3.a1
   Web of Science ®Google Scholar
• Kozumi H, Kobayashi G. Gibbs sampling methods for Bayesian quantile regression. J Stat Comput Simul. 2011;81:1565–1578. doi: 10.1080/00949655.2010.496117
   Web of Science ®Google Scholar
• Koenker RW, d'Orey V. Algorithm as 229: computing regression quantiles. Appl Stat. 1987;36:383–393. doi: 10.2307/2347802
   Web of Science ®Google Scholar
• Chen C. A finite smoothing algorithm for quantile regression. J Comput Graph Stat. 2007;16:136–164. doi: 10.1198/106186007X180336
   Web of Science ®Google Scholar
• Xu Z, Zhang H, Wang Y, et al. L1/2 regularization. Sci China Inf Sci. 2010;53:1159–1169. doi: 10.1007/s11432-010-0090-0
   Google Scholar
• Nadarajah S. Acknowledgement of priority: the generalized normal distribution. J Appl Stat. 2006;33:1031–1032. doi: 10.1080/02664760600938494
   Web of Science ®Google Scholar
• Mallick H, Yi N. Bayesian bridge regression. J Appl Stat. 2018;45:988–1008. doi: 10.1080/02664763.2017.1324565
   PubMed Web of Science ®Google Scholar
• Polson NG, Scott JG, Windle J. The Bayesian bridge. J R Stat Soc B: Stat Methodol. 2014;76:713–733. doi: 10.1111/rssb.12042
   Google Scholar
• Roberts GO, Rosenthal JS. Optimal scaling for various Metropolis-Hastings algorithms. Stat Sci. 2001;16:351–367. doi: 10.1214/ss/1015346320
   Web of Science ®Google Scholar
• Tan A, Huang J. Bayesian inference for high-dimensional linear regression under mnet priors. Can J Stat. 2016;44:180–197. doi: 10.1002/cjs.v44.2
   Web of Science ®Google Scholar
• Raftery AE, Lewis SM. [Practical Markov Chain Monte Carlo]: comment: one long run with diagnostics: implementation strategies for markov chain monte carlo. Stat Sci. 1992;7:493–497.
   Google Scholar
• Alhamzawi R. Brq: an R package for Bayesian quantile regression; 2018. (Working paper).
   Google Scholar
• Pérez-Rodríguez P, Montesinos-López OA, Montesinos-López A, et al. Bayesian regularized quantile regression: a robust alternative for genome-based prediction of skewed data. Crop J. 2020;8:713–722. doi: 10.1016/j.cj.2020.04.009
   Google Scholar
• Ouyang L, Zhu S, Ye K, et al. Robust Bayesian hierarchical modeling and inference using scale mixtures of normal distributions. IISE Trans. 2022;54:659–671.
   Web of Science ®Google Scholar
• Waldmann E, Kneib T. Bayesian bivariate quantile regression. Stat Modelling. 2015;15:326–344. doi: 10.1177/1471082X14551247
   Web of Science ®Google Scholar