Variable selection for semiparametric regression models with iterated penalisation

References

• Chen , X. 2007 . “ Large Sample Sieve Estimation of Semi-nonparametric Models ” . In Handbook of Econometrics , Edited by: Intriligator , M. D. and Griliches , Z. 48 – 59 . North Holland : Elsevier . Chapter 76
   Google Scholar
• Du , P. , Ma , S. and Liang , H. 2010 . Penalized Variable Selection Procedure for Cox Models with Semiparametric Relative Risk . Annals of Statistics , 38 ( 4 ) : 2092 – 2117 .
   PubMed Web of Science ®Google Scholar
• Fan , J. and Li , R. 2001 . Variable Selection Via Nonconcave Penalized Likelihood and its Oracle Properties . JASA , 96 ( 456 ) : 1348 – 1360 .
   Web of Science ®Google Scholar
• Friedman , J. , Hastie , T. and Tibshirani , R. 2010 . “ A Note on the Group Lasso and a Sparse Group Lasso ” . Technical Report, Stanford University, Dept. of Statistics.
   Google Scholar
• Hastie , T. , Tibshirani , R. and Friedman , J. 2009 . The Elements of Statistical Learning: Data Mining, Inference, and Prediction , New York : Springer .
   Google Scholar
• Horowitz , J. 2009 . Semiparametric and Nonparametric Methods in Economics , New York : Springer .
   Google Scholar
• Huang , J. , Ma , S. and Zhang , C. 2008a . Adaptive Lasso for High Dimensional Regression Models . Statistica Sinica , 18 ( 374 ) : 1603 – 1618 .
   Google Scholar
• Huang , J. , Horowitz , J. and Ma , S. 2008b . Asymptotic Properties of Bridge Estimators in Sparse High-dimensional Regression Models . Annals of Statistics , 36 ( 2 ) : 587 – 613 .
   Web of Science ®Google Scholar
• Li , R. and Liang , H. 2008 . Variable Selection in Semiparametric Regression Modeling . Annals of Statistics , 36 ( 1 ) : 261 – 286 .
   PubMed Web of Science ®Google Scholar
• Meier , L. , van de Geer , S. and Buhlmann , P. 2008 . The Group Lasso for Logistic Regression . JRSSB , 70 ( 1 ) : 53 – 71 .
   Google Scholar
• Meinshausen , N. 2007 . Relaxed Lasso . Computational Statistics and Data Analysis , 52 ( 1 ) : 374 – 393 .
   Web of Science ®Google Scholar
• Meinshausen , N. and Buhlmann , P. 2006 . High Dimensional Graphs and Variable Selection with the Lasso . Annals of Statistics , 34 ( 3 ) : 1436 – 1462 .
   Web of Science ®Google Scholar
• Negahban , S. , Ravikumar , P. , Wainwright , M. J. and Yu , B. 2011 . “ A Unified Framework for High-dimensional Analysis of M-estimators with Decomposable Regularizers ” . Manuscript, University of California, Berkeley, Dept. of Statistics and EECS
   Google Scholar
• Ruppert , D. , Wand , M. P. and Carroll , R. J. 2003 . Semiparametric Regression , Cambridge : Cambridge University Press .
   Google Scholar
• Schorling , J. B. , Roach , J. , Siegel , M. , Baturka , N. , Hunt , D. E. , Guterbock , T. M. and Stewart , H. L. 1997 . A Trial of Church-based Smoking Cessation Interventions for Rural African Americans . Preventive Medicine , 26 ( 1 ) : 92 – 101 .
   PubMed Web of Science ®Google Scholar
• Schumaker , L. 1981 . Spline Functions: Basic Theory , New York : Wiley .
   Google Scholar
• Tibshirani , R. 1996 . Regression Shrinkage and Selection Via the Lasso . JRSSB , 58 ( 1 ) : 267 – 288 .
   Google Scholar
• Tseng , P. 2001 . Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization . Journal of Optimization Theory and Applications , 109 ( 3 ) : 475 – 494 .
   Web of Science ®Google Scholar
• Van de Geer , S. 2008 . High Dimensional Generalized Linear Models and the Lasso . Annals of Statistics , 36 ( 2 ) : 614 – 645 .
   Web of Science ®Google Scholar
• Van der Vaart , A. W. and Wellner , J. A. 1996 . Weak Convergence and Empirical Processes , New York : Springer Verlag .
   Google Scholar
• Wand , M. P. 2003 . Smoothing and Mixed Models . Computational Statistics , 18 ( 2 ) : 223 – 249 .
   Web of Science ®Google Scholar
• Willems , J. P. , Saunders , J. T. , Hunt , D. E. and Schorling , J. B. 1997 . Prevalence of Coronary Heart Disease Risk Factors among Rural Blacks: A Community-based Study . Southern Medical Journal , 90 ( 8 ) : 814 – 820 .
   PubMed Web of Science ®Google Scholar
• Xiang , D. and Wahba , G. 1997 . Approximate Smoothing Spline Methods for Large Data Set in the Binary Case . Proceedings of the 1997 ASA Joint Statistical Meetings, Biometrics Section , : 94 – 98 .
   Google Scholar
• Xie , H. and Huang , J. 2009 . SCAD-penalized Regression in High-dimensional Partially Linear Models . Annals of Statistics , 37 ( 2 ) : 673 – 696 .
   Web of Science ®Google Scholar
• Yuan , M. and Lin , Y. 2006 . Model Selection and Estimation in Regression with Grouped Variables . JRSSB , 68 ( 1 ) : 49 – 67 .
   Google Scholar
• Zhang , C. 2010 . Nearly Unbiased Variable Selection Under Minimax Concave Penalty . Annals of Statistics , 38 ( 2 ) : 894 – 942 .
   Web of Science ®Google Scholar
• Zhang , C. and Huang , J. 2008 . The Sparsity and Bias of the Lasso Selection in High-dimensional Linear Regression . Annals of Statistics , 36 ( 4 ) : 1567 – 1594 .
   Web of Science ®Google Scholar
• Zhao , P. and Yu , B. 2006 . On Model Selection Consistency of Lasso . Journal of Machine Learning Research , 7 ( 11 ) : 2541 – 2563 .
   Google Scholar
• Zou , H. 2006 . The Adaptive Lasso and its Oracle Properties . JASA , 101 ( 476 ) : 1418 – 1429 .
   Web of Science ®Google Scholar