Testing the Goodness of Fit of a Linear Model via Nonparametric Regression Techniques

References

• Azzalini , A. , Bowman , A. and Härdle , W. 1989 . On the Use of Nonparametric Regression for Model Checking . Biometrika , 76 : 1 – 12 .
   Web of Science ®Google Scholar
• Cox , D. D. and Koh , E. 1989 . A Smoothing Spline Based Test of Model Adequacy in Polynomial Regression . Annals of the Institute of Statistical Mathematics , 41 : 383 – 400 .
   Web of Science ®Google Scholar
• Cox , D. D. , Koh , E. , Wahba , G. and Yandell , B. 1988 . Testing the (Parametric) Null Model Hypothesis in (Semiparametric) Partial and Generalized Spline Models . The Annals of Statistics , 16 : 113 – 119 .
   Web of Science ®Google Scholar
• Craven , P. and Wahba , G. 1979 . Smoothing Noisy Data With Spline Functions: Estimating the Correct Degree of Smoothing by the Method of Generalized Cross-Validation . Numerische Mathematik , 31 : 377 – 403 .
   Web of Science ®Google Scholar
• De Jong , P. 1987 . A Central Limit Theorem for Generalized Quadratic Forms . Probability Theory and Related Fields , 25 : 261 – 277 .
   Web of Science ®Google Scholar
• Demmler , A. and Reinsch , C. 1975 . Oscillation Matrices With Spline Smoothing . Numerische Mathematik , 24 : 375 – 382 .
   Web of Science ®Google Scholar
• Eubank , R. L. 1988 . Spline Smoothing and Nonparametric Regression , New York : Marcel Dekker .
   Google Scholar
• Gasser , T. , Sroka , L. and Jennen-Steinmetz , C. 1986 . Residual Variance and Residual Pattern in Nonlinear Regression . Biometrika , 73 : 625 – 633 .
   Web of Science ®Google Scholar
• Gunst , R. and Mason , R. 1980 . Regression Analysis and Its Application: A Data Oriented Approach , New York : Marcel Dekker .
   Google Scholar
• Härdle , W. and Mammen , E. 1988 . Comparing Non Parametric Versus Parametric Regression Fits unpublished manuscript
   Google Scholar
• Härdle , W. and Marron , S. Semiparametric Comparison of Regression Curves . The Annals of Statistics , 18 (in press)
   Web of Science ®Google Scholar
• Holst , L. and Rao , J. S. 1980 . Asymptotic Theory for Some Families of Two Sample Nonparametric Statistics . Sankhyâ , 42 : 19 – 52 .
   Google Scholar
• Holst , L. and Rao , J. S. 1981 . Asymptotic Spacings Theory With Applications to the Two Sample Problem . The Canadian Journal of Statistics , 9 : 79 – 89 .
   Google Scholar
• King , E. 1988 . A Test for the Equality of Two Regression Curves Based on Kernel Smoothers , Texas A&M University, Dept. of Statistics . unpublished Ph.D. dissertation
   Google Scholar
• Müller , H. G. 1989 . Goodness-of-Fit for Parametric Regression Models Via Nonparametric Regression unpublished manuscript
   Google Scholar
• Nychka , D. 1989 . Confidence Intervals for the Estimated Smoothing Parameter in Nonparametric Regression unpublished manuscript
   Google Scholar
• Raz , J. 1990 . Testing for No Effect When Estimating a Smooth Function by Nonparametric Regression: A Randomization Approach . Journal of the American Statistical Association , 85 : 132 – 138 .
   Web of Science ®Google Scholar
• Reinsch , C. 1967 . Smoothing by Spline Functions . Numerische Mathematik , 10 : 177 – 183 .
   Web of Science ®Google Scholar
• Rice , J. 1984 . Bandwidth Choice for Nonparametric Regression . The Annals of Statistics , 12 : 1215 – 1230 .
   Web of Science ®Google Scholar
• Silverman , B. 1984a . Spline Smoothing: The Equivalent Variable Kernel Method . The Annals of Statistics , 12 : 898 – 916 .
   Web of Science ®Google Scholar
• Silverman , B. 1984b . A Fast and Efficient Cross-Validation Method for Smoothing Parameter Choice in Spline Regression . Journal of the American Statistical Association , 79 : 584 – 589 .
   Web of Science ®Google Scholar
• Speckman , P. 1981 . The Asymptotic Integrated Mean Square Error for Smoothing Noisy Data by Spline Functions unpublished manuscript
   Google Scholar
• Staniswalis , J. and Severini , T. 1989 . Diagnostics for Assessing Regression Models unpublished manuscript
   Google Scholar
• Utreras , F. 1985 . On Generalized Cross-Validation for Multivariate Smoothing Spline Functions , Texas A&M University, Dept. of Mathematics . Center for Approximation Theory Report 81
   Google Scholar
• Wahba , G. and Wendelberger , J. G. 1980 . Some New Mathematical Methods for Variational Objective Analysis Using Splines and Cross-Validation . Monthly Weather Review , 108 : 1122 – 1143 .
   Web of Science ®Google Scholar