Adaptive sup-norm regularized simultaneous multiple quantiles regression

References

• R. Koenker, G. Bassett, Regression quantiles, Econometrica, 4 (1978), pp. 33–50 doi: 10.2307/1913643
   Web of Science ®Google Scholar
• W. Hendricks, R. Koenker, Hierarchical spline models for conditional quantiles and the demand for electricity, J. Am. Statist. Assoc., 87 (1992), pp. 58–68 doi: 10.1080/01621459.1992.10475175
   Web of Science ®Google Scholar
• R. Koenker, K. Hallock, Quantile regression, J. Econ. Perspect., 15 (2001), pp. 143–156 doi: 10.1257/jep.15.4.143
   Web of Science ®Google Scholar
• S. Yang, Censored median regression using weighted empirical survival and hazard functions, J. Am. Statist. Assoc., 94 (1999), pp. 137–145 doi: 10.1080/01621459.1999.10473830
   Web of Science ®Google Scholar
• R. Koenker, R. Geling, Reappraising medfly longevity: a quantile regression survival analysis, J. Am. Statist. Assoc., 96 (2001), pp. 458–468 doi: 10.1198/016214501753168172
   Web of Science ®Google Scholar
• H. Wang, X. He, Detecting differential expressions in genechip microarray studies: a quantile approach, J. Am. Statist. Assoc., 102 (2007), pp. 104–112 doi: 10.1198/016214506000001220
   Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. B, 58 (1996), pp. 267–288
   Google Scholar
• J. Fan, R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Statist. Assoc., 96 (2001), pp. 1348–1360 doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• H. Zou, The adaptive lasso and its oracle properties, J. Am. Statist. Assoc., 101 (2006), pp. 1418–1429 doi: 10.1198/016214506000000735
   Web of Science ®Google Scholar
• R. Koenker, Quantile regression for longitudinal data, J. Multivariate Anal., 91 (2004), pp. 74–89 doi: 10.1016/j.jmva.2004.05.006
   Web of Science ®Google Scholar
• C. Leng, Y. Lin, G. Wahba, A note on lasso and related procedures in model selection, Stat. Sin., 16 (2006), pp. 1273–1284
   Web of Science ®Google Scholar
• M. Yuan, Y. Lin, On the nonnegative garrote estimator, J. R. Stat. Soc. B, 69 (2007), pp. 143–161 doi: 10.1111/j.1467-9868.2007.00581.x
   Google Scholar
• Y. Wu, Y. Liu, Variable selection in quantile regression, Stat. Sin., 19 (2009), pp. 801–817
   Web of Science ®Google Scholar
• H. Wang, G. Li, G. Jiang, Robust regression shrinkage and consistent variable selection via the LAD-LASSO, J. Bus. Econ. Stat., 25 (2007), pp. 347–355 doi: 10.1198/073500106000000251
   Web of Science ®Google Scholar
• J. Xu, Z. Ying, Simultaneous estimation and variable selection in median regression using lasso-type penalty, Ann. Inst. Stat. Math., 62 (2010), pp. 487–514 doi: 10.1007/s10463-008-0184-2
   PubMed Web of Science ®Google Scholar
• L. Breiman, J. H. Friedman, Predicting multivariate responses in multiple linear regression, J. R. Stat. Soc. B, 59 (1997), pp. 3–54 doi: 10.1111/1467-9868.00054
   Google Scholar
• B. Turlach, W. Venables, S. Wright, Simultaneous variable selection, Technometrics, 47 (2005), pp. 349–363 doi: 10.1198/004017005000000139
   Web of Science ®Google Scholar
• T. Similä, J. Tikka, Input selection and shrinkage in multiresponse linear regression, Comput. Stat. Data Anal., 52 (2007), pp. 406–422 doi: 10.1016/j.csda.2007.01.025
   Web of Science ®Google Scholar
• M. Yuan, Y. Lin, Model selection and estimation in regression with grouped variables, J. R. Stat. Soc. B, 68 (2006), pp. 49–67 doi: 10.1111/j.1467-9868.2005.00532.x
   Google Scholar
• H. Zou, M. Yuan, Regularized simultaneous model selection in multiple quantiles regression, Comput. Stat. Data Anal., 52 (2008), pp. 5296–5304 doi: 10.1016/j.csda.2008.05.013
   Web of Science ®Google Scholar
• H. Zhang, Y. Liu, Y. Wu, J. Zhu, Variable selection for multicategory svm via sup-norm regularization, Electron. J. Stat., 2 (2008), pp. 149–167 doi: 10.1214/08-EJS122
   Web of Science ®Google Scholar
• H. Zou, M. Yuan, The F∞-norm support vector machine, Stat. Sin., 18 (2008), pp. 379–398
   Web of Science ®Google Scholar
• S. Bang, M. Jhun, Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization, Comput. Stat. Data Anal., 56 (2012), pp. 813–826 doi: 10.1016/j.csda.2011.01.026
   Web of Science ®Google Scholar
• R. Koenker, Quantile Regression, Cambridge University Press, New York, (2005)
   Google Scholar
• H. Wang, C. Leng, A note on adaptive group lasso, Comput. Stat. Data Anal., 52 (2008), pp. 5277–5286 doi: 10.1016/j.csda.2008.05.006
   Web of Science ®Google Scholar
• G. Schwarz, Estimating the dimension of a model, Ann. Stat., 6 (1978), pp. 461–464 doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• M. Yuan, GACV for quantile smoothing splines, Comput. Stat. Data Anal., 50 (2006), pp. 813–829 doi: 10.1016/j.csda.2004.10.008
   Web of Science ®Google Scholar
• R. Koenker, P. Ng, S. Portnoy, Quantile smoothing splines, Biometrika, 81 (1994), pp. 673–680 doi: 10.1093/biomet/81.4.673
   Web of Science ®Google Scholar
• Y. Li, J. Zhu, The l1 norm quantile regression, J. Comput. Graph. Stat., 17 (2008), pp. 163–185 doi: 10.1198/106186008X289155
   Web of Science ®Google Scholar
• I. Takeuchi, Q. V. Le, T. D. Sears, A. J. Smola, Nonparametric quantile estimation, J. Mach. Learn. Res., 7 (2006), pp. 1231–1264
   Web of Science ®Google Scholar
• Y. Wu, Y. Liu, Stepwise multiple quantile regression estimation using non-crossing constraints, Stat. Interface, 2 (2009), pp. 299–310 doi: 10.4310/SII.2009.v2.n3.a4
   Web of Science ®Google Scholar
• H. D. Bondell, B. J. Reich, H. Wang, Non-crossing quantile regression curve estimation, Biometrika, 97 (2010), pp. 825–838 doi: 10.1093/biomet/asq048
   PubMed Web of Science ®Google Scholar
• Y. Liu, Y. Wu, Simultaneous multiple non-crossing quantile regression estimation using kernel constraints, J. Nonparametric Stat., 23 (2011), pp. 415–437 doi: 10.1080/10485252.2010.537336
   PubMed Web of Science ®Google Scholar
• B. Skagerberg, J. MacGregor, C. Kiparissides, Multivariate data analysis applied to low-density polyethylene reactors, Chemometr. Intell. Lab. Syst., 14 (1992), pp. 341–356 doi: 10.1016/0169-7439(92)80117-M
   Web of Science ®Google Scholar
• R. W. Johnson, Fitting percentage of body fat to simple body measurements, J. Stat. Educ., 4 (1996), pp. 1–7
   Google Scholar
• C. J. Gyer, On the asymptotics of constrained m-estimation, Ann. Stat., 22 (1994), pp. 1993–2010 doi: 10.1214/aos/1176325768
   Web of Science ®Google Scholar
• K. Knight, Limiting distributions for l1 regression estimators under general conditions, Ann. Stat., 26 (1998), pp. 755–770 doi: 10.1214/aos/1028144858
   Web of Science ®Google Scholar