Determination of linear components in additive models

References

• Aerts , M. , Claeskens , G. and Wand , M. P. 2002 . Some Theory for Penalized Spline Generalized Additive Models . Journal of Statistical Planning and Inference , 103 : 455 – 470 .
   Google Scholar
• Aitken , A. C. 1950 . On the Statistical Independence of Quadratic Forms in Normal Variates . Biometrika , 37 : 93 – 96 .
   PubMed Web of Science ®Google Scholar
• Barry , D. 1993 . Testing for Additivity of a Regression Function . The Annals of Statistics , 21 : 235 – 254 .
   Web of Science ®Google Scholar
• de Boor , C. 2001 . A Practical Guide to Splines , New York : Springer-Verlag .
   Google Scholar
• Box , G. E. 1954 . Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification . The Annals of Mathematical Statistics , 25 : 290 – 302 .
   Google Scholar
• Brumback , B. A. , Ruppert , D. and Wand , M. 1999 . Comment on “Variable Selection and Function Estimation in Additive Nonparametric Regression Using a Data-based Prior” by Shively, Kohn and Wood . Journal of the American Statistical Association , 94 : 794 – 797 .
   Web of Science ®Google Scholar
• Cai , Z. W. , Fan , J. Q. and Li , R. Z. 2000 . Efficient Estimation and Inferences for Varying-Coefficient Models . Journal of the American Statistical Association , 95 : 888 – 902 .
   Web of Science ®Google Scholar
• Chen , R. , Liu , J. S. and Tsay , R. S. 1995 . Additivity Tests for Nonlinear Autoregressive Models . Biometrika , 82 : 369 – 383 .
   Web of Science ®Google Scholar
• Claeskens , G. 2004 . Restricted Likelihood Ratio Lack-of-Fit Tests Using Mixed Spline Models . Journal of the Royal Statistical Society, Series B , 66 : 909 – 926 .
   Google Scholar
• Claeskens , G. , Krivobokova , T. and Opsomer , J. 2008 . Asymptotic Properties of Penalized Spline Estimator . Biometrika , 96 : 529 – 544 .
   Web of Science ®Google Scholar
• Crainiceanu , C. M. and Ruppert , D. 2003 . Likelihood Ratio Tests in Linear Mixed Models with One Variance Component . Journal of the Royal Statistical Society, Series B , 66 : 165 – 185 .
   Google Scholar
• Crainiceanu , C. M. , Ruppert , D. and Vogelsang , T. J. 2003 . Some Properties of Likelihood Ratio Tests in Linear Mixed Models . manuscript, www.orie.cornell.edu/~davidr/papers
   Google Scholar
• Crainiceanu , C. , Ruppert , D. , Claeskens , G. and Wand , M. P. 2005 . Exact Likelihood Ratio Test for Penalized Splines . Biometrika , 92 : 91 – 103 .
   Web of Science ®Google Scholar
• Cushman , M. , Kuller , L. H. , Prentice , R. , Rodabough , R. J. , Psaty , B. M. , Stafford , R. S. , Sidney , S. and Rosendaal , R. F. 2004 . Estrogen Plus Progestin and Risk of Venous Thrombosis . Journal of the American Medical Association , 292 : 1573 – 1580 . and for the Women's Health Initiative Investigators
   PubMed Web of Science ®Google Scholar
• Dominici , F. , McDermott , A. , Zeger , S. L. and Samet , J. M. 2002 . On the Use of Generalized Additive Models in Time-Series of Air Pollution and Health . American Journal of Epidemiology , 156 : 193 – 203 .
   PubMed Web of Science ®Google Scholar
• Eilers , P. H.C. and Marx , B. D. 1996 . Flexible Smoothing with B-Splines and Penalties (with comments) . Statistical Science , 11 : 89 – 121 .
   Web of Science ®Google Scholar
• Eubank , R. L. and Speigelman , C. 1990 . Testing the Goodness-of-Fit Linear Models Via Nonparametric Regression Techniques . Journal of the American Statistical Association , 85 : 387 – 392 .
   Web of Science ®Google Scholar
• Hall , P. and Opsomer , J. D. 2005 . Theory for Penalised Spline Regression . Biometrika , 92 : 105 – 118 .
   Web of Science ®Google Scholar
• Härdle , W. and Mammen , E. 1993 . Comparing Nonparametric Versus Parametric Regression Fits . The Annals of Statistics , 21 : 1926 – 1947 .
   Web of Science ®Google Scholar
• Härdle , W. and Marron , S. 1991 . Bootstrap Simultaneous Error Rates for Nonparametric Regression . The Annals of Statistics , 19 : 778 – 796 .
   Web of Science ®Google Scholar
• Härdle , W. and Tsybakov , A. B. 1995 . Additive Nonparametric Regression on Principal Components . Journal of Nonparametric Statistics , 5 : 157 – 184 .
   Google Scholar
• Härdle , W. , Liang , H. and Gao , J. T. 2000 . Partially Linear Models , Heidelberg : Springer Physica-Verlag .
   Google Scholar
• Härdle , W. , Huet , S. , Mammen , E. and Sperlich , S. 2004 . Bootstrap Inference in Semiparametric Generalized Additive Models . Econometric Theory , 20 : 265 – 300 .
   Web of Science ®Google Scholar
• Härdle , W. , Müller , M. , Sperlich , S. and Werwatz , A. 2004 . Nonparametric and Semiparametric Models , Heidelberg : Springer Verlag .
   Google Scholar
• Hastie , T. J. and Tibshirani , R. J. 1990 . Generalized Additive Model , London : Chapman and Hall .
   Google Scholar
• Hastie , T. J. and Tibshirani , R. J. 1993 . Varying-Coefficient Models (with discussion) . Journal of the Royal Statistical Society, Series B , 55 : 757 – 796 .
   Google Scholar
• Hauser , R. , Meeker , J. D. , Duty , S. , Silva , M. J. and Calafat , A. M. 2006 . Altered Semen Quality in Relation to Urinary Concentrations of Phthalate Monoester and Oxidative Metabolites . Epidemiology , 17 : 682 – 691 .
   PubMed Web of Science ®Google Scholar
• Hjellvik , V. and Tjøstheim , D. 1996 . Nonparametric Statistics for Testing of Linearity and Serial Independence . Journal of Nonparametric Statistics , 6 : 223 – 251 .
   Google Scholar
• Hsu , C. C. , Kao , L. W.H. , Coresh , J. , Pankow , J. S. , Marsh-Manzi , J. , Boerwinkle , E. and Bray , M. S. 2005 . Apolipoprotein E and Progression of Chronic Kidney Disease . Journal of the American Medical Association , 93 : 2892 – 2899 .
   Google Scholar
• Huang , J. Z. 2003 . Local Asymptotics for Polynomial Spline Regression . The Annals of Statistics , 31 : 1600 – 1625 .
   Web of Science ®Google Scholar
• Huang , L. S. and Chen , J. 2008 . Analysis of Variance, Coefficient of Determination, and F-test for Local Polynomial Regression . The Annals of Statistics , 36 : 2085 – 2109 .
   Web of Science ®Google Scholar
• Ichimura , H. 1993 . Semiparametric Least Squares (SLS) and Weighted SLS Estimation of Single-Index Models . Journal of Econometrics , 58 : 71 – 120 .
   Web of Science ®Google Scholar
• Li , Q. and Rachine , J. S. 2007 . Nonparametric Econometrics: Theory and Practice , Princeton : Princeton University Press .
   Google Scholar
• Li , Y. and Ruppert , D. 2008 . On the Asymptotics of Penalized Splines . Biometrika , 95 : 415 – 436 .
   Web of Science ®Google Scholar
• Liang , H. , Thurston , S. , Ruppert , D. , Apanasovich , T. and Hauser , R. 2008 . Additive Partial Linear Models with Measurement Errors . Biometrika , 95 : 667 – 678 .
   Web of Science ®Google Scholar
• Linton , O. B. and Nielsen , J. P. 1995 . A Kernel Method of Estimating Structured Nonparametric Regression Based on Marginal Integration . Biometrika , 82 : 93 – 101 .
   Web of Science ®Google Scholar
• Liu , R. and Yang , L. 2010 . Spline-Backfitted Kernel Smoothing of Additive Coefficient Model . Econometric Theory , 26 : 29 – 59 .
   Web of Science ®Google Scholar
• Ma , S. and Yang , L. 2011 . Spline-Backfitted Kernel Smoothing of Partially Linear Additive Model . Journal of Statistical Planning and Inference , 141 : 204 – 219 .
   Web of Science ®Google Scholar
• Mardia , K. V. , Kent , J. T. and Bibby , J. M. 1979 . Multivariate Analysis , New York : Academic Press .
   Google Scholar
• Opsomer , J. D. , Claeskens , G. , Ranalli , M. G. , Kauermann , G. and Breidt , F. J. 2008 . Non-parametric Small Area Estimation Using Penalized Spline Regression . Journal of the Royal Statistical Society, Series B , 70 : 265 – 286 .
   Google Scholar
• Ruppert , D. 2002 . Selecting the Number of Knots for Penalized Splines . Journal Computational and Graphical Statistics , 11 : 735 – 757 .
   Web of Science ®Google Scholar
• Ruppert , D. and Carroll , R. 2000 . Spatially-Adaptive Penalties for Spline Fitting . Australian Journal of Statistics , 42 : 205 – 223 .
   Google Scholar
• Ruppert , D. , Wand , M. and Carroll , R. 2003 . Semiparametric Regression , New York : Cambridge University Press .
   Google Scholar
• Self , S. and Liang , K. 1987 . Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions . Journal of the American Statistical Association , 82 : 605 – 610 .
   Web of Science ®Google Scholar
• Song , Q. and Yang , L. 2010 . Oracally Efficient Spline Smoothing of Nonlinear Additive Autoregression Models with Simultaneous Confidence Band . Journal of Multivariate Analysis , 101 : 2008 – 2025 .
   Web of Science ®Google Scholar
• Sperlich , S. , Tjøstheim , D. and Yang , L. 2002 . Nonparametric Estimation and Testing of Interaction in Additive Models . Econometric Theory , 18 : 197 – 251 .
   Web of Science ®Google Scholar
• Stone , C. J. 1986 . The Dimensionality Reduction Principle for Generalized Additive Models . The Annals of Statistics , 14 : 590 – 606 .
   Web of Science ®Google Scholar
• Wahba, G. (1990), Spline Models for Observational Data, CBMS-NSF Regional Conference Series in Applied Mathematics, 59. Society for Industrial and Applied Mathematics (SIAM)
   Google Scholar
• Wand , M. P. 1999 . On the Optimal Amount of Smoothing in Penalized Spline Regression . Biometrika , 86 : 936 – 940 .
   Web of Science ®Google Scholar
• Wang , L. and Yang , L. 2007 . Spline-Backfitted Kernel Smoothing of Nonlinear Additive Autoregression Model . The Annals of Statistics , 35 : 2474 – 2503 .
   Web of Science ®Google Scholar
• Wu , C. F.J. 1986 . Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis . The Annals of Statistics , 14 : 1261 – 1343 .
   Web of Science ®Google Scholar
• Xia , Y. , Zhang , W. and Tong , H. 2004 . Efficient Estimation for Semivarying-Coefficient Models . Biometrika , 91 : 661 – 681 .
   Web of Science ®Google Scholar
• Yu , Y. and Ruppert , D. 2002 . Penalized Spline Estimation for Partially Linear Single Index Models . Journal of the American Statistical Association , 97 : 1042 – 1054 .
   Web of Science ®Google Scholar