SCAD-penalised generalised additive models with non-polynomial dimensionality

References

• Chen , J. and Chen , Z. 2008 . Extended Bayesian Information Criteria for Model Selection with Large Model Spaces . Biometrika , 95 ( 3 ) : 759 – 771 .
   Web of Science ®Google Scholar
• Chen , J. and Chen , Z. 2012 . Extended BIC for Small-n-Large-p Sparse GLM . Statistica Sinica , 22 : 555 – 574 .
   Web of Science ®Google Scholar
• Costessi , A. , Mahrour , N. , Tijchon , E. , Stunnenberg , R. , Stoel , M. , Jansen , P. , Sela , D. , Martin-Brown , S. , Washburn , M. , Florens , L. , Conaway , J. W. , Conaway , R. C. and Stunnenberg , H. G. 2011 . The Tumour Antigen PRAME is a Subunit of a Cul2 Ubiquitin Ligase and Associates with Active NFY Promoters . The EMBO Journal , 30 ( 18 ) : 3786 – 3798 .
   Web of Science ®Google Scholar
• Fan , J. Q. and Li , R. Z. 2001 . Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties . Journal of the American Statistical Association , 96 ( 456 ) : 1348 – 1360 .
   Web of Science ®Google Scholar
• Fan , J. Q. and Lv , J. 2011 . Non-Concave Penalized Likelihood with NP-Dimensionality . IEEE Transactions on Information Theory , 57 ( 8 ) : 5467 – 5484 .
   PubMed Web of Science ®Google Scholar
• Frank , I. and Friedman , J. 1993 . A Statistical View of Some Chemometrics Regression Tools . Technometrics , 35 : 109 – 135 .
   Web of Science ®Google Scholar
• van der Geer , S. A. 2000 . Applications of Empirical Process Theory , Cambridge , MA : Cambridge University Press .
   Google Scholar
• Hastie , T. and Tibshirani , R. 1990 . Generalized Additive Models , 1 , London, New York : Chapman and Hall . Monographs on statistics and applied probability
   Google Scholar
• Huang , J. , Horowitz , J. L. and Ma , S. G. 2008 . Asymptotic Properties of Bridge Estimators in Sparse High-Dimensional Regression Models . Annals of Statistics , 36 ( 2 ) : 587 – 613 .
   Web of Science ®Google Scholar
• Huang , J. , Horowitz , J. L. and Wei , F. 2010 . Variable Selection in Nonparametric Additive Models . Annals of Statistics , 38 ( 4 ) : 2282 – 2313 .
   PubMed Web of Science ®Google Scholar
• Kim , Y. , Choi , H. and Oh , H. 2008 . Smoothly Clipped Absolute Deviation on High Dimensions . Journal of the American Statistical Association , 103 ( 484 ) : 1665 – 1673 .
   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
• Lian , H. 2012 . Variable Selection for High-Dimensional Generalized Varying-Coefficient Models . Statistica Sinica , to appear.
   Web of Science ®Google Scholar
• McCullagh , P. and Nelder , J. A. 1989 . Generalized Linear Models , 2 , London, New York : Chapman and Hall .
   Google Scholar
• Storlie , C. , Bondell , H. , Reich , B. and Zhang , H. 2011 . Surface Estimation, Variable Selection, and the Nonparametric Oracle Property . Statistica Sinica , 21 : 679 – 705 .
   PubMed Web of Science ®Google Scholar
• Tibshirani , R. 1996 . Regression Shrinkage and Selection via the Lasso . Journal of the Royal Statistical Society Series B – Methodological , 58 ( 1 ) : 267 – 288 .
   Google Scholar
• van't Veer , L. , Dai , H. , van de Vijver , M. , He , Y. , Hart , A. , Mao , M. , Peterse , H. , van der Kooy , K. , Marton , M. , Witteveen , A. , Schreiber , G. J. , Kerkhoven , R. M. , Roberts , C. , Linsley , P. S. , Bernards , R. and Friend , S. H. 2002 . Gene Expression Profiling Predicts Clinical Outcome of Breast Cancer . Nature , 415 ( 6871 ) : 530 – 536 .
   PubMed Web of Science ®Google Scholar
• Wang , H. S. and Xia , Y. C. 2009 . Shrinkage Estimation of the Varying Coefficient Model . Journal of the American Statistical Association , 104 ( 486 ) : 747 – 757 .
   Web of Science ®Google Scholar
• Wang , H. , Li , R. and Tsai , C. L. 2007 . Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method . Biometrika , 94 ( 3 ) : 553 – 568 .
   PubMed Web of Science ®Google Scholar
• Wang , L. F. , Li , H. Z. and Huang , J. H.Z. 2008 . Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements . Journal of the American Statistical Association , 103 ( 484 ) : 1556 – 1569 .
   PubMed Web of Science ®Google Scholar
• Wang , H. S. , Li , B. and Leng , C. L. 2009 . Shrinkage Tuning Parameter Selection with a Diverging Number of Parameters . Journal of the Royal Statistical Society Series B – Statistical Methodology , 71 : 671 – 683 .
   Web of Science ®Google Scholar
• Wang , L. , Liu , X. , Liang , H. and Carroll , R. 2011 . Estimation and Variable Selection for Generalized Additive Partially Linear Models . Annals of Statistics , 39 ( 4 ) : 1827 – 1851 .
   PubMed Web of Science ®Google Scholar
• Wei , F. , Huang , J. and Li , H. 2011 . Variable Selection and Estimation in High-Dimensional Varying-Coefficient Models . Statistica Sinica , 21 : 1515 – 1540 .
   PubMed Web of Science ®Google Scholar
• Xie , H. L. 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
• Zhu , L. and Zhu , L. 2009 . Nonconcave Penalized Inverse Regression in Single-Index Models with High-Dimensional Predictors . Journal of Multivariate Analysis , 100 ( 5 ) : 862 – 875 .
   Web of Science ®Google Scholar
• Zou , H. 2006 . The Adaptive Lasso and Its Oracle Properties . Journal of the American Statistical Association , 101 ( 476 ) : 1418 – 1429 .
   Web of Science ®Google Scholar