Variable Selection in Additive Models Using P-Splines

References

• Antoniadis , A. , Gijbels , I. and Nikolova , M. 2011 . “Penalized Likelihood Regression for Generalized Linear Models With Nonquadratic Penalties,” . The Annals of the Institute of Statistical Mathematics , 63 : 585 – 615 .
   Web of Science ®Google Scholar
• Belge , M. , Kilmer , M. E. and Miller , E. L. 2002 . “Efficient Determination of Multiple Regularization Parameters in a Generalized L-Curve Approach,” . Inverse Problems , 18 : 1161 – 1183 .
   Web of Science ®Google Scholar
• Breiman , L. 1995 . “Better Subset Regression Using the Nonnegative Garrote,” . Technometrics , 51 : 373 – 384 .
   Google Scholar
• Cantoni , E. , Flemming , J. and Ronchetti , E. 2011 . “Variable Selection in Additive Models by Nonnegative Garrote,” . Statistical Modelling , 11 : 237 – 252 .
   Web of Science ®Google Scholar
• Chien , W.-H. , Chen , L. , Wei , C.-C. , Hsu , H.-H. and Wang , T.-S. 2010 . “Modeling Slump Flow of High-Performance Concrete Using a Back-Propagation Network,” . Applied Mechanics and Materials , 20–23 : 838 – 842 .
   Google Scholar
• Claeskens , G. , Krivobokova , T. and Opsomer , J. D. 2009 . “Asymptotic Properties of Penalized Spline Estimators,” . Biometrika , 96 : 529 – 544 .
   Web of Science ®Google Scholar
• Eilers , P. and Marx , B. 1996 . “Flexible Smoothing With B-Splines and Penalties,” . Statistical Science , 11 : 89 – 102 .
   Web of Science ®Google Scholar
• Eubank , R. L. and Speckman , P. 1990 . “Curve Fitting by Polynomial-Trigonometric Regression,” . Biometrika , 77 : 1 – 9 .
   Web of Science ®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
• Frank , A. and Asuncion , A. 2010 . UCI Machine Learning Repository. “Concrete Slump Test Data Set” . [online]. Available at http://archive.ics.uci.edu/ml.
   Google Scholar
• Gijbels , I. and Verhasselt , A. 2010a . “P-Splines Regression Smoothing and Difference Type of Penalty,” . Statistics and Computing , 20 : 499 – 511 .
   Web of Science ®Google Scholar
• Gijbels , I. and Verhasselt , A. 2010b . “Regularisation and P-Splines in Generalised Linear Models,” . Journal of Nonparametric Statistics , 22 : 271 – 295 .
   Web of Science ®Google Scholar
• Hastie , T. , Tibshirani , R. and Friedman , J. 2009 . The Elements of Statistical Learning: Data Mining, Inference and Prediction (2nd ed.) , New York : Springer .
   Google Scholar
• Horowitz , J. , Klemelä , J. and Mammen , E. 2006 . “Optimal Estimation in Ddditive Regression Models,” . Bernoulli , 12 : 271 – 298 .
   Web of Science ®Google Scholar
• Huang , J. , Horowitz , J. and Wei , F. 2010 . “Variable Selection in Nonparametric Additive Models,” . The Annals of Statistics , 38 : 2282 – 2313 .
   PubMed Web of Science ®Google Scholar
• Lin , B. Y. and Zhang , H. H. 2006 . “Component Selection and Smoothing in Multivariate Nonparametric Regression,” . The Annals of Statistics , 32 : 2272 – 2297 .
   Google Scholar
• Marx , B. and Eilers , P. 2005 . “Multidimensional Penalized Signal Regression,” . Technometrics , 47 : 13 – 22 .
   Web of Science ®Google Scholar
• Reich , B. , Storlie , C. B. and Bondell , H. D. 2009 . “Variable Selection in Bayesian Smoothing Spline ANOVA Models: Application to Deterministic Computer Codes,” . Technometrics , 51 : 110 – 120 .
   PubMed Web of Science ®Google Scholar
• Ruppert , D. , Wand , M. and Carroll , R. J. 2003 . Semiparametric Regression , Cambridge : Cambridge University Press .
   Google Scholar
• Stamey , T. , Kabalin , J. , McNeal , J. , Johnston , I. , Freiha , F. , Redwine , E. and Yang , N. 1989 . “Prostate Specific Antigen in the Diagnosis and Treatment of Adenocarcinoma of the Prostate, ii: Radical Prostatectomy Treated Patients,” . Journal of Urology , 16 : 1076 – 1083 .
   Web of Science ®Google Scholar
• Storlie , C. , Bondell , H. , Reich , B. and Zhang , H. 2011 . “Surface Estimation, Variable Selection, and the Nonparametric Oracle Property,” . Statistica Sinica , 21 : 697 – 705 .
   Google Scholar
• Vaughn , P. , Bean , J. E. , Helton , J. C. , Lord , M. E. , MacKinnon , R. J. and Schreiber , J. D. 2000 . “Representation of Two-Phase Flow in the Vicinity of the Repository in the 1996 Performance Assessment for the Waste Isolation Pilot Plant,” . Reliability Engineering and System Safety , 69 : 205 – 226 .
   Google Scholar
• Wang , L. , Li , H. and Huang , J. Z. 2008 . “Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements,” . Journal of the American Statistical Association , 103 : 1556 – 1569 .
   PubMed Web of Science ®Google Scholar
• Xiong , S. 2010 . “Some Notes on the Nonnegative Garrote,” . Technometrics , 52 : 349 – 361 .
   Web of Science ®Google Scholar
• Yeh , I. 2007 . “Modeling Slump Flow of Concrete Using Second-Order Regressions and Artificial Neural Networks,” . Cement and Concrete Composites , 29 : 474 – 480 .
   Web of Science ®Google Scholar
• Yuan , M. 2007 . “Nonnegative Garrote Component Selection in Functional ANOVA models,” . Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics March 21–24, 2007, San Juan, Puerto Rico , 2 : 660 – 666 .
   Google Scholar
• Zou , H. 2006 . “The Adaptive Lasso and Its Oracle Pproperties,” . Journal of the American Statistical Association , 101 : 1418 – 1429 .
   Web of Science ®Google Scholar