References
- Andrews, D. F., & Mallows, C. L. (1974). Scale mixtures of normal distributions. Journal of the Royal Statistical Society. Series B (Methodological), 36(3), 99–102. https://doi.org/10.1111/rssb.1974.36 [Crossref], [Google Scholar]
- Cheng, C. I., & Speckman, P. L. (2012). Bayesian smoothing spline analysis of variance. Computational Statistics and Data Analysis, 56(12), 3945–3958. https://doi.org/10.1016/j.csda.2012.05.020 [Crossref], [Web of Science ®], [Google Scholar]
- Chernozhukov, V. (2005). Extremal quantile regression. Annals of Statistics, 33(2), 806–839. https://doi.org/10.1214/009053604000001165 [Crossref], [Web of Science ®], [Google Scholar]
- Cole, T. J. (1988). Fitting smoothed centile curves to reference data. Journal of the Royal Statistical Society. Series A, 151(3), 385–418. https://doi.org/10.2307/2982992 [Crossref], [Web of Science ®], [Google Scholar]
- Craven, P., & Wahba, G. (1978). Smoothing noisy data with spline functions. Numerische Mathematik, 31(4), 377–403. https://doi.org/10.1007/BF01404567 [Crossref], [Web of Science ®], [Google Scholar]
- de Oliveira, V. (2007). Objective Bayesian analysis of spatial data with measurement error. The Canadian Journal of Statistics , 35(2), 283–301. https://doi.org/10.1002/cjs.v35:2 [Crossref], [Web of Science ®], [Google Scholar]
- Gordon, P. (1941). Values of Mills' ratio of area to bounding ordinate and of the normal probability integral for large values of the argument. Annals of Mathematical Statistics, 12(3), 364–366. https://doi.org/10.1214/aoms/1177731721 [Crossref], [Google Scholar]
- Gu, C. (2013). Smoothing spline ANOVA models (2nd ed.). Springer. [Crossref], [Google Scholar]
- Hobert, J. P., & Casella, G. (1996). The effect of improper priors on Gibbs sampling in hierarchical linear mixed models. Journal of the American Statistical Association, 91(436), 1461–1473. https://doi.org/10.1080/01621459.1996.10476714 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Hu, Y., Zhao, K., & Lian, H. (2015). Bayesian quantile regression for partially linear additive models. Statistics and Computing, 25(3), 651–668. https://doi.org/10.1007/s11222-013-9446-9 [Crossref], [Web of Science ®], [Google Scholar]
- Jone, M. C. (1988). Discussion of paper by T. J. Cole. Journal of the Royal Statistical Society. Series A, 151(3), 412–413. https://doi.org/10.2307/2982992 [Google Scholar]
- Jørgensen, B. (1982). Statistical properties of the generalized inverse Gaussian distribution. Springer-Verlag New York Inc. [Crossref], [Google Scholar]
- Jullion, R., & Lambert, P. (2007). Robust specification of the roughness penalty prior distribution in spatially adaptive Bayesian P-splines models. Computational Statistics and Data Analysis, 51(5), 2542–2558. https://doi.org/10.1016/j.csda.2006.09.027 [Crossref], [Web of Science ®], [Google Scholar]
- Koenker, R. (2004). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74–89. https://doi.org/10.1016/j.jmva.2004.05.006 [Crossref], [Web of Science ®], [Google Scholar]
- Koenker, R. (2005). Quantile regression. Cambridge University Press. [Crossref], [Google Scholar]
- Koenker, R., & Bassett, G. (1978). Regression quantiles. Econometrica, 46(1), 33–50. https://doi.org/10.2307/1913643 [Crossref], [Web of Science ®], [Google Scholar]
- Koenker, R., Ng, P., & Portnoy, S. (1994). Quantile smoothing splines. Biometrika, 81(4), 673–680. https://doi.org/10.1093/biomet/81.4.673 [Crossref], [Web of Science ®], [Google Scholar]
- Kozumi, H., & Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation, 81(11), 1565–1578. https://doi.org/10.1080/00949655.2010.496117 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Lang, S., & Brezger, A. (2004). Bayesian P-Splines. Journal of Computational and Graphical Statistics, 13(1), 183–212. https://doi.org/10.1198/1061860043010 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Li, Y, & Zhu, J. (2008). L1-Norm quantile regression. Journal of Computational and Graphical Statistics, 17(1), 163–185. https://doi.org/10.1198/106186008X289155 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Liu, Y., & Wu, Y. (2011). Simultaneous multiple non-crossing quantile regression estimation using kernel constraints. Journal of Nonparametric Statistic, 23(2), 415–437. https://doi.org/10.1080/10485252.2010.537336 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Nelson, C. B., & Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of Business, 60(4), 473–489. https://doi.org/10.1086/jb.1987.60 [Crossref], [Web of Science ®], [Google Scholar]
- Nychka, D. (2000). Smoothing and regression: approaches, computation, and application. Wiley. [Google Scholar]
- Santos, B, & Bolfarine, H. (2016). On Bayesian quantile regression and outliers. https://arxiv.org/pdf/1601.07344.pdf [Crossref], [Google Scholar]
- Silverman, B. (1985). Some aspects of the spline smoothing approach to non-parametric regression curve fitting. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 47(1), 1–52. https://doi.org/10.1111/j.2517-6161.1985.tb01327.x [Crossref], [Web of Science ®], [Google Scholar]
- Speckman, L. P., & Sun, D. (2003). Fully Bayesian spline smoothing and intrinsic autoregressive prior. Biometrika, 90(2), 289–302. https://doi.org/10.1093/biomet/90.2.289 [Crossref], [Web of Science ®], [Google Scholar]
- Sriram, K., Ramamoorthi, R. V., & Ghosh, P. (2013). Posterior consistency of bayesian quantile regression based on the misspecified asymmetric laplace density. Bayesian Analysis, 8(2), 479–504. https://doi.org/10.1214/13-BA817 [Crossref], [Web of Science ®], [Google Scholar]
- Sun, D., & Speckman, L. P. (2008). Bayesian hierarchical linear mixed models for additive smoothing splines. Annals of the Institute of Statistical Mathematics, 60(3), 499–517. https://doi.org/10.1007/s10463-007-0127-3 [Crossref], [Web of Science ®], [Google Scholar]
- Sun, D., Tsutakawa, R. K., & Speckman, P. L. (1999). Posterior distribution of hierarchical models using CAR(1) distributions. Biometrika, 86(2), 41–50. https://doi.org/10.1093/biomet/86.2.341 [Crossref], [Web of Science ®], [Google Scholar]
- Svensson, L. E. (1994). Estimating and interpreting forward interest rates: Sweden 1992–1994. Technical Report, NBER Working Paper, 4871, 1–27. https://doi.org/10.3386/w4871 [Google Scholar]
- Thompson, P., Cai, Y., Moyeed, R., Reeve, D., & Stander, J. (2010). Bayesian nonparametric quantile regression using splines. Computational Statistics and Data Analysis, 54(4), 1138–1150. https://doi.org/10.1016/j.csda.2009.09.004 [Crossref], [Web of Science ®], [Google Scholar]
- Tong, X., He, Z., & Sun, D. (2018). Estimating Chinese treasury yield curves with Bayesian smoothing splines. Econometrics and Statistics, 8, 94–124. https://doi.org/10.1016/j.ecosta.2017.10.001 [Crossref], [Web of Science ®], [Google Scholar]
- van Dyk, D. A., & Park, T. (2008). Partially collapsed gibbs samplers. Journal of the American Statistical Association, 103(482), 790–796. https://doi.org/10.1198/016214508000000409 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Wahba, G. (1990). Spline models for observational data. Society for Industrial and Applied Mathematics. [Crossref], [Google Scholar]
- Wang, H., Li, G., & Jiang, G. (2007). Robust regression shrinkage and consistent variable selection through the LAD-Lasso. Journal of Business and Economic Statistics, 25(3), 347–355. https://doi.org/10.1198/073500106000000251 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Wu, Y, & Liu, Y. (2009). Variable selection in quantile regression. Statistica Sinica, 19(2), 801–817. [Web of Science ®], [Google Scholar]
- Yu, K., & Moyeed, R. A. (2001). Bayesian quantile regression. Statistics and Probability Letters, 54(4), 437–447. https://doi.org/10.1016/S0167-7152(01)00124-9 [Crossref], [Web of Science ®], [Google Scholar]
- Yuan, M. (2006). GACV for quantile smoothing splines. Computational Statistics and Data Analysis, 5(3), 813–829. https://doi.org/10.1016/j.csda.2004.10.008 [Crossref], [Google Scholar]
- Yue, Y. R., & Rue, H. (2011). Bayesian inference for additive mixed quantile regression models. Computational Statistics and Data Analysis, 55(1), 84–96. https://doi.org/10.1016/j.csda.2010.05.006 [Crossref], [Web of Science ®], [Google Scholar]
- Zhang, F. (2011). Matrix theory-basic results and techniques. Springer. [Crossref], [Google Scholar]