An Analysis of Transformations for Additive Nonparametric Regression

References

• Amemiya , T. and Powell , J. L. 1981 . “A Comparison of the Box-Cox Maximum Likelihood Estimator and the Non-Linear Two-Stage Least Squares Estimator,” . Journal of Econometrics , 17 : 351 – 381 .
   Web of Science ®Google Scholar
• Andrews , D. W. K. 1995 . “Nonparametric Kernel Estimation for Semiparametric Models,” . Econometric Theory , 11 : 560 – 596 .
   Web of Science ®Google Scholar
• Angrist , J. D. , Imbens , G. W. and Rubin , D. B. 1996 . “Identification of Causal Effects Using Instrumental Variables,” (with discussion) . Journal of the American Statistical Association , 91 : 444 – 472 .
   Web of Science ®Google Scholar
• Auestad , B. and Tjøstheim , D. 1991 . “Functional Identification in Nonlinear Time Series,” . In Nonparametric Functional Estimation and Related Topics , Edited by: Roussas , G. 493 – 507 . Dordrecht : Kluwer .
   Google Scholar
• Berndt , E. 1991 . The Practice of Econometrics , Reading , MA : Addison-Wesley .
   Google Scholar
• Bickel , P. J. and Doksum , K. A. 1981 . “An Analysis of Transformations Revisited,” . Journal of the American Statistical Association , 76 : 296 – 311 .
   Web of Science ®Google Scholar
• Bickel , P. J. , Klaassen , C. A. J. , Ritov , Y. and Wellner , J. A. 1993 . Efficient and Adaptive Inference in Semiparametric Models , Baltimore : Johns Hopkins University, Press .
   Google Scholar
• Box , G. E. P. and Cox , D. R. 1964 . “An Analysis of Transformations” . Journal of the Royal Statistical Society , 26 : 211 – 252 . Ser. B
   Google Scholar
• Breiman , L. and Friedman , J. H. 1985 . “Estimating Optimal Transformations for Multiple Regression and Correlation,” (with discussion) . Journal of the American Statistical Association , 80 : 580 – 619 .
   Web of Science ®Google Scholar
• Burbidge , J. B. , Magee , L. and Robb , A. L. 1988 . “Alternative Transformations to Handle Extreme Values of the Dependent Variable,” . Journal of the American Statistical Association , 83 : 123 – 127 .
   Web of Science ®Google Scholar
• Buja , A. , Hastie , T. and Tibshirani , R. 1989 . “Linear Smoothers and Additive Models,” (with discussion) . The Annals of Statistics , 17 : 453 – 555 .
   Web of Science ®Google Scholar
• Carroll , R. J. 1980 . “A Robust Method of Testing Transformations to Achieve Approximate Normality,” . Journal of the Royal Statistical Society , 42 : 71 – 78 . Ser. B
   Google Scholar
• Carroll , R. J. 1982 . “Prediction and Power Transformations When the Choice of Power is Restricted to a Finite Set,” . Journal of the American Statistical Association , 77 : 908 – 915 .
   Web of Science ®Google Scholar
• Carroll , R. J. and Ruppert , D. 1984 . “Power Transformation When Fitting Theoretical Models to Data,” . Journal of the American Statistical Association , 79 : 321 – 328 .
   Web of Science ®Google Scholar
• Carroll , R. J. and Ruppert , D. 1988 . Transformation and Weighting in Regression , New York : Chapman and Hall .
   Google Scholar
• Carroll , R. J. and Wand , M. P. 1991 . “Semiparametric Estimation in Logistic Measurement Error Models,” . Journal of the Royal Statistical Society , 53 : 573 – 585 . Ser. B
   Google Scholar
• Chen , R. , Härdle , W. , Linton , O. B. and Severance-Lossin , E. “Estimation in Additive Nonparametric Regression,” . Proceedings of the COMPSTAT Conference Semmering . Edited by: Härdle , W. and Schimek , M. Heidelberg : Physika Verlag .
   Google Scholar
• Ehrlich , I. 1977 . “Capital Punishment and Deterrence: Some Further Thoughts and Additional Evidence,” . Journal of Political Economy , 85 : 741 – 788 .
   Web of Science ®Google Scholar
• Engle , R. F. , Granger , C. W. J. , Rice , J. and Weiss , A. 1986 . “Semiparametric Estimates of the Relation Between Weather and Electricity Sales,” . Journal of the American Statistical Association , 81 : 310 – 320 .
   Web of Science ®Google Scholar
• Fan , J. 1992 . “Design-Adaptive Nonparametric Regression,” . Journal of the American Statistical Association , 87 : 998 – 1004 .
   Web of Science ®Google Scholar
• Fan , J. , Härdle , W. and Mammen , E. “Direct Estimation of Low-Dimensional Components in Additive Models,” (in press), submitted to The Annals of Statistics.
   Google Scholar
• Gutierrez , R. and Carroll , R. J. 1995 . “Plug-In Semiparametric Estimating Equations,” , Texas A&M University . unpublished manuscript
   Google Scholar
• Härdle , W. 1990 . Applied Nonparametric Regression , Cambridge , , U.K. : Cambridge University Press .
   Google Scholar
• Hastie , T. J. and Tibshirani , R. J. 1990 . Generalized Additive Models , London : Chapman and Hall .
   Google Scholar
• Heckman , J. J. and Polachek , S. 1974 . “Empirical Evidence on the Functional Form of the Earnings-Schooling Relationship,” . Journal of the American Statistical Association , 69 : 350 – 354 .
   Web of Science ®Google Scholar
• Hengartner , N. W. 1996 . “Rate-Optimal Estimation of Additive Regression via the Integration Method in the Presence of Many Covariates,” , Yale University, Dept. of Statistics . preprint
   Google Scholar
• Hinkley , D. V. and Runger , G. 1984 . “The Analysis of Transformed Data” (with discussion) . Journal of the American Statistical Association , 79 : 302 – 320 .
   Web of Science ®Google Scholar
• Hulten , C. R. and Wykoff , F. C. 1981 . “The Estimation of Economic Depreciation Using Vintage Asset Prices,” . Journal of Econometrics , 15 : 367 – 396 .
   Web of Science ®Google Scholar
• Ibragimov , I. A. and Hasminskii , R. Z. 1980 . “On Nonparametric Estimation of Regression,” . Soviet Mathematics. Doklady , 21 : 810 – 4 .
   Google Scholar
• Johnson , N. L. 1949 . “Systems of Frequency Curves Generated by Methods of Translation,” . Biometrika , 36 : 149 – 176 .
   PubMed Web of Science ®Google Scholar
• Linton , O. B. and Härdle , W. 1996 . “Estimating Additive Regression With Known Links,” . Biometrika , 83 : 529 – 540 .
   Web of Science ®Google Scholar
• Linton , O. B. and Nielsen , J. P. 1995 . “Estimating Structured Nonparametric Regression of the Kernel Method,” . Biometrika , 82 : 93 – 101 .
   Web of Science ®Google Scholar
• Mukarjee , H. and Stern , S. 1994 . “Feasible Nonparametric Estimation of Multiargument Monotone Functions,” . Journal of the American Statistical Association , 89 : 77 – 80 .
   Web of Science ®Google Scholar
• Newey , W. K. 1990 . “Semiparametric Efficiency Bounds,” . Journal of Applied Econometrics , 5 : 99 – 135 .
   Web of Science ®Google Scholar
• Newey , W. K. 1991 . “Uniform Convergence in Probability and Stochastic Equicontinuity,” . Econometrica , 59 : 1161 – 1168 .
   Web of Science ®Google Scholar
• Newey , W. K. 1994 . “Kernel Estimation of Partial Means,” . Econometric Theory , 10 : 233 – 253 .
   Web of Science ®Google Scholar
• Newey , W. K. and McFadden , D. 1994 . “Large Sample Estimation and Hypothesis Testing,” . In Handbook of Econometrics , Edited by: Engle , R. F. and McFadden , D. L. Vol. 4 , Amsterdam : Elsevier .
   Google Scholar
• Robins , J. , Rotnizky , A. and Zhao , L. 1994 . “Estimation of Regression Coefficients When Some Regressors are not Always Observed,” . Journal of the American Statistical Association , 89 : 846 – 857 .
   Web of Science ®Google Scholar
• Robinson , P. M. 1988 . “Root-n-Consistent Semiparametric Regression,” . Econometrica , 56 : 931 – 954 .
   Web of Science ®Google Scholar
• Robinson , P. M. 1991 . “Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models,” . Econometrica , 59 : 755 – 786 .
   Web of Science ®Google Scholar
• Stone , C. J. 1980 . “Optimal Rates of Convergence for Nonparametric Estimators,” . The Annals of Statistics , 8 : 1348 – 1360 .
   Web of Science ®Google Scholar
• Stone , C. J. 1982 . “Optimal Global Rates of Convergence for Nonparametric Regression,” . The Annals of Statistics , 8 : 1040 – 1053 .
   Web of Science ®Google Scholar
• Stone , C. J. 1986 . “The Dimensionality Reduction Principle for Generalized Additive Models,” . The Annals of Statistics , 14 : 592 – 606 .
   Web of Science ®Google Scholar
• Tibshirani , R. 1988 . “Estimating Optimal Transformations for Regression via Additivity and Variance Stabilization,” . Journal of the American Statistical Association , 83 : 394 – 405 .
   Web of Science ®Google Scholar
• Tjøstheim , D. and Auestad , B. 1994 . “Nonparametric Identification of Nonlinear Time Series: Projections,” . Journal of the American Statistical Association , 89 : 1398 – 1409 .
   Web of Science ®Google Scholar
• Wang , N. and Ruppert , D. 1996 . “Estimation of Regression Parameters in a Semiparametric Transformation Model,” . Journal of Statistical Planning and Inference , 52 : 331 – 351 .
   Web of Science ®Google Scholar
• Zarembka , P. 1968 . “Functional Form in the Demand for Money,” . Journal of the American Statistical Association , 63 : 502 – 511 .
   Web of Science ®Google Scholar
• Zarembka , P. 1974 . “Transformations of Variables in Econometrics,” . In Frontiers in Econometrics , Edited by: Zarembka , P. Boston : Academic Press .
   Google Scholar
• Zellner , A. and Revankar , N. 1969 . “Generalized Production Functions,” . Review of Economic Studies , 37 : 241 – 250 .
   Web of Science ®Google Scholar