Simultaneous multiple non-crossing quantile regression estimation using kernel constraints

References

• Bondell , H. D. , Reich , B. J. and Wang , H. 2010 . Non-Crossing Quantile Regression Curve Estimation . Biometrika , in press
   PubMed Web of Science ®Google Scholar
• Brown , M. P.S. , Grundy , W. N. , Lin , D. , Cristianini , N. , Sugnet , C. W. , Furey , T. S. , Ares , M. and Haussler , D. 2000 . Knowledge-Based Analysis of Microarray Gene Expression Data by using Support Vector Machines . Proceedings of the National Academy of Science , 97 : 262 – 267 .
   PubMed Web of Science ®Google Scholar
• Chernozhukov , V. , Fernandez-Val , I. and Galichon , A. 2009 . Quantile and Probability Curves without Crossing arXiv:0704.3649
   Google Scholar
• Dette , H. and Volgushev , S. 2008 . Non-crossing Non-parametric Estimates of Quantile Curves . Journal of Royal Statistical Society, Ser. B , 70 : 609 – 627 .
   Google Scholar
• Fan , J. and Li , R. 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
• Hall , P. , Wolff , R. C.L. and Yao , Q. 1999 . Methods for Estimating a Conditional Distribution Function . Journal of American Statistical Association , 94 : 154 – 163 .
   Web of Science ®Google Scholar
• He , X. 1997 . Quantile Curves without Crossing . American Statistician , 51 : 186 – 192 .
   Web of Science ®Google Scholar
• He , X. , Ng , P. and Portnoy , S. 1998 . Bivariate Quantile Smoothing Splines . Journal of the Royal Statistical Society, Ser. B , 60 : 537 – 550 .
   Google Scholar
• Kimeldorf , G. and Wahba , G. 1971 . Some Results on Tchebycheffian Spline Functions . Journal of Mathematical Analysis and Applications , 33 : 82 – 95 .
   Web of Science ®Google Scholar
• Koenker , R. 2004 . Quantile Regression for Longitudinal Data . Journal of Multivariate Analysis , 91 : 74 – 89 .
   Web of Science ®Google Scholar
• Koenker , R. 2005 . Quantile Regression (Econometric Society Monographs) , New York, NY : Cambridge University Press .
   Google Scholar
• Koenker , R. and Bassett , G. 1978 . Regression Quantiles . Econometrica , 46 : 33 – 50 .
   Web of Science ®Google Scholar
• Koenker , R. , Ng , P. and Portnoy , S. 1994 . Quantile Smoothing Splines . Biometrika , 81 : 673 – 680 .
   Web of Science ®Google Scholar
• Leeb , H. and Potscher , B. M. 2008 . Sparse Estimators and the Oracle Property, or the Return of Hodge's Estimator . Journal of Econometrics , 142 : 201 – 211 .
   Web of Science ®Google Scholar
• Li , Y. and Zhu , J. 2008 . L1-norm Quantile Regression . Journal of Computational and Graphical Statistics , 17 : 163 – 185 .
   Web of Science ®Google Scholar
• Li , Y. , Liu , Y. and Zhu , J. 2007 . Quantile Regression in Reproducing Kernel Hilbert Spaces . Journal of the American Statistical Association , 102 : 255 – 268 .
   Web of Science ®Google Scholar
• Liu , Y. , Shen , X. and Doss , H. 2005 . Multicategory ψ-learning and Support Vector Machine: Computational Tools . Journal of Computational and Graphical Statistics , 14 : 219 – 236 .
   Web of Science ®Google Scholar
• Neocleousa , T. and Portnoy , S. 2007 . On Monotonicity of Regression Quantile Functions . Statistics and Probability Letters , 78 : 1226 – 1229 .
   Web of Science ®Google Scholar
• Potscher , B. M. and Leeb , H. 2009 . On the Distribution of Penalized Maximum Likelihood Estimators: The Lasso, Scad, and Thresholding . Journal of Multivariate Analysis , 100 : 2065 – 2082 .
   Web of Science ®Google Scholar
• Potscher , B. M. and Schneider , U. 2010 . Confidence Sets Based on Penalized Maximum Likelihood Estimators in Gaussian Regression . Electronic Journal of Statistics , 4 : 334 – 360 .
   Web of Science ®Google Scholar
• Scholkopf , B. and Smola , A. 2002 . Learning with Kernels Support Vector Machines, Regularization, Optimization and Beyond , Cambridge, MA : MIT Press .
   Google Scholar
• Schwarz , G. 1978 . Estimating the Dimension of a Model . Annals of Statistics , 6 : 461 – 464 .
   Web of Science ®Google Scholar
• Shim , J. , Hwang , C. and Seok , K. H. 2009 . Non-crossing Quantile Regression via Doubly Penalized Kernel Machine . Computational Statistics , 24 : 83 – 94 .
   Web of Science ®Google Scholar
• Takeuchi , I. and Furuhashi , T. 2004 . Non-crossing Quantile Regressions by svm . Proceedings of the International Joint Conference on Neural Networks , : 401 – 406 .
   Google Scholar
• Takeuchi , I. , Le , Q. V. , Sears , T. D. and Smola , A. J. 2006 . Nonparametric Quantile Estimation . Journal of Machine Learning Research , 7 : 1231 – 1264 .
   Web of Science ®Google Scholar
• Tibshirani , R. J. 1996 . Regression Shrinkage and Selection via the Lasso . Journal of the Royal Statistical Society, Ser. B , 58 : 267 – 288 .
   Google Scholar
• Wang , H. , Li , G. and Jiang , G. 2007 . Robust Regression Shrinkage and Consistent Variable Selection Through the Lad-Lasso . Journal of Business and Economic Statistics , 25 : 347 – 355 .
   Web of Science ®Google Scholar
• Wu , Y. and Liu , Y. 2008 . Variable Selection in Quantile Regression . Statistica Sinica , 19 : 801 – 817 .
   Web of Science ®Google Scholar
• Wu , Y. and Liu , Y. 2009 . Stepwise Multiple Quantile Regression Estimation using Non-crossing Constraints . Statistics and Its Interface , 2 : 299 – 310 .
   Web of Science ®Google Scholar
• Yu , K. and Jones , M. C. 1998 . Local Linear Quantile Regression . Journal of American Statistical Association , 93 : 228 – 237 .
   Web of Science ®Google Scholar
• Yuan , M. 1978 . Gacv for Quantile Smoothing Splines . Computational Statistics and Data Analysis , 5 : 813 – 829 .
   Google Scholar
• Zhang , H. H. , Liu , Y. , Wu , Y. and Zhu , J. 2008 . Multicategory Sup-norm Support Vector Machines . Electronic Journal of Statistics , 2 : 149 – 167 .
   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. and Li , R. 2008 . One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models (with Discussion) . Annals of Statistics , 36 : 1509 – 1566 .
   PubMed Web of Science ®Google Scholar
• Zou , H. and Yuan , M. 2008a . Composite Quantile Regression and the Oracle Model Selection Theory . Annals of Statistics , 36 : 1108 – 1126 .
   Web of Science ®Google Scholar
• Zou , H. and Yuan , M. 2008b . Regularized Simultaneous Model Selection in Multiple Quantiles Regression . Computational Statistics and Data Analysis , 52 : 5296 – 5304 .
   Web of Science ®Google Scholar