Bayesian Elastic Net Tobit Quantile Regression

References

• Akaike, H. (1973). Information theory and an extension of maximum likelihood principle. In: Petrov, B. N., Csaki, F., eds.Second International Symposium on Information Theory. Budapest: Akademiai Kiado.
   Google Scholar
• Alhamzawi, R. (2013). Tobit quantile regression with the adaptive lasso penalty. The Fourth International Arab Conference of Statistics, 450 ISSN (1681 6870).
   Google Scholar
• Alhamzawi, R., Yu, K. (2013). Conjugate priors and variable selection for Bayesian quantile regression. Computational Statistics & Data Analysis 64:209–219.
   Web of Science ®Google Scholar
• Alhamzawi, R., Yu, K., Benoit, D.F. (2012). Bayesian adaptive Lasso quantile regression. Statistical Modelling 12:279–297.
   Web of Science ®Google Scholar
• Chen, M., Carlson, D., Zaas, A., Woods, C., Ginsburg, G.S., Lucas, J., Carin, L. (2011). Detection of viruses via statistical gene expression analysis. IEEE Transactions on Biomedical Engineering 58:468–479.
   PubMed Web of Science ®Google Scholar
• Chernozhukov, V., Hong, H. (2002). Three-step censored quantile regression and extramarital affairs. Journal of the American Statistical Association 86:87297–882.
   Google Scholar
• Chhikara, R., Folks, L. (1989). The Inverse Gaussian Distribution: Theory, Methodology, and Applications. New York: Marcel Dekker.
   Google Scholar
• Efron, B., Hastie, T., Johnstone, I., Tibshirani, R. (2004). Least angle regression (with discussion). The Annals of Statistics 32:407–451.
   Web of Science ®Google Scholar
• Fair, R. (1978). Theory of extramarital affairs. Journal of Political Economy 86:45–61.
   Web of Science ®Google Scholar
• Fan, J., Li, R.Z. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96:1348–1360.
   Web of Science ®Google Scholar
• Gilks, W.R. (1992). Derivative-free adaptive rejection sampling for Gibbs sampling. In: Bernardo, J., Berger, J., Dawid, A. P., Smith, A. F. M., eds. Bayesian Statistics 4. Oxford University Press, pp. 641–649.
   Google Scholar
• Griffin, J.E., Brown, P.J. (2010). Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis 1:171–188.
   Web of Science ®Google Scholar
• Hashem, H., Vinciotti, V., Alhamzawi, R., Yu, K. (2013). Bayesian tobit quantile regression with group lasso penalty. Technical report, Department of Mathematics. School of Information Systems, Computing and Mathematics. Brunel University.
   Google Scholar
• Ji, Y., Lin, N., Zhang, B. (2012). Model selection in binary and Tobit quantile regression using the Gibbs sampler. Computational Statistics & Data Analysis 56:827–839.
   Web of Science ®Google Scholar
• Kinney, S.K., Dunson, D.B. (2007). Fixed and random effects selection in linear and logistic models. Biometrics 63:690–698.
   PubMed Web of Science ®Google Scholar
• Kocherginsky, M., He, X., Mu, Y. (2005). Practical confidence intervals for regression quantiles. Journal of Computational and Graphical Statistics 14:41–55.
   Web of Science ®Google Scholar
• Koenker, R. (2005). Quantile Regression. Cambridge Books: Cambridge University Press.
   Google Scholar
• Koenker, R. (2011). quantreg: Quantile regression. R package version 4.71.
   Google Scholar
• Koenker, R., Bassett, G.J. (1978). Regression quantiles. Econometrica 46:33–50.
   Web of Science ®Google Scholar
• Koenker, R., D’Orey, V. (1987). Algorithm AS 229: Computing regression quantiles. Journal of the Royal Statistical Society: Series C (Applied Statistics) 36:383–393.
   Web of Science ®Google Scholar
• Kozumi, H., Kobayashi, G. (2011). Gibbs sampling methods for Bayesian quantile regression. Journal of Statistical Computation and Simulation 81:1565–1578.
   Web of Science ®Google Scholar
• Li, Q., Xi, R., Lin, N. (2010). Bayesian regularized quantile regression. Bayesian Analysis 5:533–556.
   Web of Science ®Google Scholar
• Li, Y., Zhu, J. (2008). l1-norm quantile regressions. Journal of Computational and Graphical Statistics 17:163–185.
   Web of Science ®Google Scholar
• Park, T., Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association 103:681–686.
   Web of Science ®Google Scholar
• Powell, J. (1986). Censored regression quantiles. Journal of Econometrics 32:143–155.
   Web of Science ®Google Scholar
• Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics 6:461–464.
   Web of Science ®Google Scholar
• Sun, W., Ibrahim, J.G., Zou, F. (2010). Genomewide multiple-loci mapping in experimental crosses by iterative adaptive penalized regression. Genetics 185:349–359.
   PubMed Web of Science ®Google Scholar
• Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society, Series B 58:267–288.
   Google Scholar
• Trautmann, H., Steyer, D., Meramann, O. (2010). truncnorm: Truncated normal distribution. R package version 1.0-4.
   Google Scholar
• Wang, H., Leng, C. (2007). Unified Lasso estimation by least squares approximation. Journal of the American Statistical Association 102:1039–1048.
   Web of Science ®Google Scholar
• Yi, N., Xu, S. (2008). Bayesian Lasso for quantitative trait loci mapping. Genetics 179:1045–1055.
   PubMed Web of Science ®Google Scholar
• Yu, K., Stander, J. (2007). Bayesian analysis of a Tobit quantile regression model. Journal of Econometrics 137:260–276.
   Web of Science ®Google Scholar
• Yuan, Y., Yin, G. (2010). Bayesian quantile regression for longitudinal studies with nonignorable missing data. Biometrics 66:105–114.
   PubMed Web of Science ®Google Scholar
• Yue, Y. R., Hong, H. G. (2012). Bayesian tobit quantile regression model for medical expenditure panel survey data. Statistical Modelling 12(4):323–346.
   Web of Science ®Google Scholar
• Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association 101:1418–1429.
   Web of Science ®Google Scholar
• Zou, H., Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B 67:301–320.
   Google Scholar
• Zou, H., Zhang, H.H. (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics 37:1733–1751.
   PubMed Web of Science ®Google Scholar