Comparing Methods for Multivariate Nonparametric Regression

References

• Banks , D. L. , Olszewski , R. T. and Maxion , R. A. 1999 . “ Comparing Methods for Multivariate Nonparametric Regression ” . Department of Computer Science Technical Report CMU-CS-99-102: Carnegie Mellon University, Pittsburgh, Pennsylvania, available in electronic format at http://reports-archive.adm.cs.cmu.edu/anon/1999/abstracts/99-102.html
   Google Scholar
• Barron , A. R. 1991 . “ Complexity regularization with applications to artificial neural networks ” . In Nonparametric Functional Estimation Edited by: Roussas , G. 561 – 576 . Dordrecht, , The Netherlands : Kluwer .
   Google Scholar
• Barron , A. R. 1993 . Universal approximation bounds for superpositions of a sigmoidal function . IEEE Transactions on Information Theory , 39 : 930 – 945 .
   Google Scholar
• Barron , A. R. and Barron , R. L. 1998 . “ Statistical learning networks: a unifying view ” . In Computing Science and Statistics , Proceedings of the Twentieth Symposium on the Interface Edited by: Wegman , E. J. , Gantz , D. T. and Miller , J. J. 192 – 203 . Alexandria, Virginia : American Statistical Association .
   Google Scholar
• Barron , A. R. and Xiao , X. 1991 . Discussion of “multivariate adaptive regression splines” by Friedman, J. H. . Annals of Statistics , 19 : 67 – 81 .
   Google Scholar
• Breiman , L. 1991 . Discussion of “multivariate adaptive regression splines” by Friedman, J. H. . Annals of Statistics , 19 : 82 – 90 .
   Google Scholar
• Breiman , L. 1991 . The II method for estimating multivariate functions from noisy data . Technometrics , 33 : 124 – 144 .
   Google Scholar
• Breiman , L. and Friedman , J. 1985 . Estimating optimal transformations for multiple regression and correlation (with discussion) . Journal of the American Statistical Association , 80 : 580 – 619 .
   Google Scholar
• Breiman , L. , Friedman , J. , Olshen , R. A. and Stone , C. 1984 . Classification and Regression Trees Belmont, California : Wadsworth .
   Google Scholar
• Buja , A. , Hastie , T. J. and Tibshirani , R. 1989 . Linear smoothers and additive models (with discussion) . Annals of Statistics , 17 : 453 – 555 .
   Google Scholar
• Buja , A. and Kass , R. 1985 . Discussion of “estimating optimal transformations for multiple regression and correlation” by Breiman, L., Friedman, J. . Journal of the American Statistical Association , 80 : 602 – 607 .
   Google Scholar
• Cleveland , W. 1979 . Robust locally weighted regression and smoothing scatterplots . Journal of the American Statistical Association , 74 : 829 – 836 .
   Google Scholar
• Cleveland , W. and Devlin , S. 1988 . Locally weighted regression: an approach to regression analysis by local fitting . Journal of the American Statistical Association , 83 : 596 – 610 .
   Google Scholar
• De Veaux , R. D. , Psichogios , D. C. and Ungar , L. H. 1993 . A comparison of two nonparametric estimation schemes: MARS and neural networks . Computers in Chemical Engineering , 17 : 819 – 837 .
   Google Scholar
• Doering , A. , Galicki , M. and Witte , H. 1997 . “ Admissibility and optimality of the cascade-correlation algorithm ” . In Artificial Neural Networks , Proceedings of the Seventh International Conference Edited by: Gerstner , W. , Germond , A. , Hasler , M. and Nicoud , J.-D. 505 – 510 . Berlin : Springer-Verlag .
   Google Scholar
• Donoho , D. L. and Johnstone , I. 1989 . Projection based approximation and a duality with kernel methods . Annals of Statistics , 17 : 58 – 106 .
   Google Scholar
• Fahlman , S. E. and Lebiere , C. 1990 . “ The cascade-correlation learning architecture ” . In Advance in Neural Information Processing Systems 2 Edited by: Touretzky , D. pp. 525 – 533 . San Mateo, California : Morgan Kaufman .
   Google Scholar
• Flury , B. 1988 . Common Principal Components and Related Multivariate Models New York : Wiley .
   Google Scholar
• Frank , I. and Friedman , J. H. 1993 . A statistical view of some chemometric regression tools (with discussion) . Technometrics , 35 : 109 – 148 .
   Google Scholar
• Friedman , J. H. 1991 . Discussion of “The II method for estimating multivariate functions from noisy data” by Breiman, L. . Technometrics , 33 : 145 – 148 .
   Google Scholar
• Friedman , J. H. 1991 . Multivariate additive regression splines . Annals. of Statistics , 19 : 1 – 66 .
   Google Scholar
• Friedman , J. H. and Stuetzle , W. 1981 . Projection pursuit regression . Journal of the American Statistical Association , 76 : 817 – 823 .
   Google Scholar
• Gu , C. 1991 . Discussion of “The II method for estimating multivariate functions from noisy data” by Breiman, L. . Technometrics , 33 : 149 – 154 .
   Google Scholar
• Gu , C. and Wahba , G. 1991 . Discussion of “multivariate adaptive regression splines” by Friedman, J. H. . Annals of Statistics , 19 : 115 – 123 .
   Google Scholar
• Hastie , T. J. and Tibshirani , R. J. 1990 . Generalized Additive Models New York : Chapman and Hall .
   Google Scholar
• Owen , A. B. 1991 . Discussion of “multivariate adaptive regression Splines” by Friedman, J. H. . Annals of Statistics , 19 : 102 – 112 .
   Google Scholar
• Ripley , B. D. 1993 . “ Statistical aspects of neural networks ” . In Networks and Chaos—Statistical and Probabilistic Aspects Edited by: Barndorff-Nielsen , O. E. , Jensen , J. L. and Kendall , W. S. pp. 40 – 123 . London : Chapman and Hall .
   Google Scholar
• Ripley , B. D. 1994a . “ Flexible non-linear approaches to classification ” . In From Statistics to Neural Networks Theory and Pattern Recognition Applications Edited by: Cherkassky , V. , Friedman , J. H. and Wechsler , H. pp. 105 – 126 . Berlin : Springer-Verlag .
   Google Scholar
• Ripley , B. D. 1994b . Neural networks and related methods for classification (with discussion) . Journal of the Royal Statistical Society, Series B , 56 : 409 – 456 .
   Google Scholar
• Ripley , B. D. 1996 . Pattern Recognition and Neural Networks Cambridge, , England : Cambridge University Press .
   Google Scholar
• Scott , D. W. 1992 . Multivariate Density Estimation New York : Wiley .
   Google Scholar
• Scott , D. W. and Wand , M. P. 1991 . Feasibility of multivariate density estimates . Biometrika , 78 : 197 – 206 .
   Google Scholar
• Sutherland , A. , Henery , R. , Molina , R. , Taylor , C. C. and King , R. 1993 . “ Statistical methods in learning ” . In IPMU'92—Advanced Methods in Artificial Intelligence Edited by: Bouchon-Meunier , B. , Valverde , L. and Yager , R. R. pp. 173 – 182 . Berlin : Springer-Verlag .
   Google Scholar
• Tibshirani , R. 1988 . Estimating optimal transformations for regression via additivity and variance stabilization . Journal of the American Statistical Association , 83 : 394 – 405 .
   Google Scholar
• Zhao , Y. and Atkeson , C. G. 1992 . “ Some approximation properties of projection pursuit networks ” . In Advances in Neural Information Processing Systems 4 Edited by: Moody , J. , Hanson , S. J. and Lippmann , R. P. pp. 936 – 943 . San Mateo, California : Morgan Kaufmann .
   Google Scholar