Investigating Smooth Multiple Regression by the Method of Average Derivatives

References

• Beran , R. 1977 . “Adaptive Estimates for Autoregressive Processes,” . Annals of the Institute of Statistical Mathematics , 28 : 77 – 89 .
   Web of Science ®Google Scholar
• Bickel , P. 1982 . “On Adaptive Estimation,” . The Annals of Statistics , 10 : 647 – 671 .
   Web of Science ®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,” . Journal of the American Statistical Association , 80 : 580 – 619 .
   Web of Science ®Google Scholar
• Carroll , R. J. 1982 . “Adapting for Heteroscedasticity in Linear Models,” . The Annals of Statistics , 10 : 1224 – 1233 .
   Web of Science ®Google Scholar
• Collomb , G. and Härdle , W. 1986 . “Strong Uniform Convergence Rates in Robust Nonparametric Time Series Analysis and Prediction: Kernel Regression Estimation From Dependent Observations,” . Stochastic Processes and Their Applications , 23 : 77 – 89 .
   Web of Science ®Google Scholar
• Friedman , J. H. and Stuetzle , W. 1981 . “Projection Pursuit Regression,” . Journal of the American Statistical Association , 76 : 817 – 823 .
   Web of Science ®Google Scholar
• Härdle , W. 1988 . “XploRe—A Computing Environment for Exploratory Regression and Density Smoothing,” . Statistical Software Newsletters , 14 : 113 – 119 .
   Google Scholar
• Härdle , W. , Hildenbrand , W. and Jerison , M. 1988 . “Empirical Evidence on the Law of Demand,” , Universität Bonn . working paper (Sonderforschungsbereich 303)
   Google Scholar
• Härdle , W. and Marron , J. S. 1987 . “Semiparametric Comparison of Regression Curves,” , Universität Bonn . working paper (Sonderforschungsbereich 303)
   Google Scholar
• Hastie , T. and Tibshirani , R. 1986 . “Generalized Additive Models” . Statistical Science , 1 : 297 – 318 . (with discussion)
   Google Scholar
• Ichimura , H. 1987 . “Estimation of Single Index Models,” , Massachusetts Institute of Technology, Dept. of Economics . unpublished doctoral dissertation
   Google Scholar
• Kallieris , D. , Mattern , R. and Härdle , W. 1989 . “Verhalten des EUROSID Beim 90 Grad Seitenaufprall im Vergleich zu PMTO Sowie US—SID, HYBRID II und APROD,” . In Forschungsvereinigung Automobiltechnik (FAT) Schriftenreihe Frankfurt am Main
   Google Scholar
• Manski , C. F. 1984 . “Adaptive Estimation of Nonlinear Regression Models,” . Econometric Reviews , 3 : 145 – 194 .
   Google Scholar
• Manski , C. F. and McFadden , D. 1981 . Structural Analysis of Discrete Data With Econometric Applications , Cambridge , MA : MIT Press .
   Google Scholar
• McCullagh , P. and Nelder , J. A. 1983 . Generalized Linear Models , London : Chapman & Hall .
   Google Scholar
• Nolan , D. and Pollard , D. 1987 . “U-Processes: Rates of Convergence,” . The Annals of Statistics , 15 : 780 – 799 .
   Web of Science ®Google Scholar
• O'Sullivan , F. , Yandell , B. S. and Raynor , W. J. 1986 . “Automatic Smoothing of Regression Functions in Generalized Linear Models,” . Journal of the American Statistical Association , 81 : 96 – 103 .
   Web of Science ®Google Scholar
• Powell , J. L. 1986 . “Symmetrically Trimmed Least Squares Estimation for Tobit Models,” . Econometrica , 54 : 1435 – 1460 .
   Web of Science ®Google Scholar
• Powell , J. L. , Stock , J. H. and Stoker , T. M. “Semiparametric Estimation of Index Coefficients,” . Econometrica , 57 (in press)
   Web of Science ®Google Scholar
• Robinson , P. M. 1988 . “Root N-Consistent Semiparametric Regression,” . Econometrica , 56 : 931 – 954 .
   Web of Science ®Google Scholar
• Schuster , E. F. 1972 . “Joint Asymptotic Distribution of the Estimated Regression Function at a Finite Number of Distinct Points,” . The Annals of Mathematical Statistics , 43 : 84 – 88 .
   Google Scholar
• Silverman , B. W. 1978 . “Weak and Strong Uniform Consistency of the Kernel Estimate of a Density Function and Its Derivatives,” . The Annals of Statistics , 6 : 177 – 184 . Addendum (1980), 8, 1175–1176
   Web of Science ®Google Scholar
• Stoker , T. M. 1986 . “Consistent Estimation of Scaled Coefficients,” . Econometrica , 54 : 1461 – 1481 .
   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. 1986 . “The Dimensionality Reduction Principle for Generalized Additive Models,” . The Annals of Statistics , 14 : 590 – 606 .
   Web of Science ®Google Scholar