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Original Articles

Estimating Optimal Transformations for Multiple Regression and Correlation

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Pages 580-598 | Received 01 Aug 1982, Published online: 12 Mar 2012

References

  • Anscombe , F. J. and Tukey , J. W. 1963 . “The Examination and Analysis of Residuals” . Technometrics , 5 : 141 – 160 .
  • Belsley , D. A. , Kuh , E. and Welsch , R. E. 1980 . Regression Diagnostics , New York : John Wiley .
  • Box , G. E. P. and Cox , D. R. 1964 . “An Analysis of Transformations” . Journal of the Royal Statistical Society , 26 : 211 – 252 . Ser. B
  • Box , G. E. P. and Hill , W. J. 1974 . “Correcting Inhomogeneity of Variance With Power Transformation Weighting” . Technometrics , 16 : 385 – 389 .
  • Box , G. E. P. and Tidwell , P. W. 1962 . “Transformations of the Independent Variables” . Technometrics , 4 : 531 – 550 .
  • Breiman , L. and Friedman , J. 1982 . “Estimating Optimal Transformations for Multiple Regression and Correlation” , Berkeley, Dept. of Statistics . Technical Report 9, University of California
  • Cleveland , W. S. 1979 . “Robust Locally Weighted Regression and Smoothing Scatterplots” . Journal of the American Statistical Association , 74 : 828 – 836 .
  • 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 : 317 – 403 .
  • Csáki , P. and Fisher , J. 1963 . “On the General Notion of Maximal Correlation” . Magyar Tudomanyos Akademia, Budapest, Matematikai Kotato Intezet, Kozlemenyei , 8 : 27 – 51 .
  • DeBoor , C. 1978 . A Practical Guide to Splines , New York : Springer-Verlag .
  • De Leeuw , J. , Young , F. W. and Takane , Y. 1976 . “Additive Structure in Qualitative Data: An Alternating Least Squares Method With Optimal Scaling Features” . Psychometrika , 41 : 471 – 503 .
  • Devroye , L. 1981 . “On the Almost Everywhere Convergence of Nonparametric Regression Function Estimates” . The Annals of Statistics , 9 : 1310 – 1319 .
  • Devroye , L. and Wagner , T. J. 1980 . “Distribution-Free Consistency Results in Nonparametric Discrimination and Regression Function Estimation” . The Annals of Statistics , 8 : 231 – 239 .
  • Efron , B. 1979 . “Bootstrap Methods: Another Look at the Jackknife” . The Annals of Statistics , 7 : 1 – 26 .
  • Fraser , D. A. S. 1967 . “Data Transformations and the Linear Model” . Annals of Mathematical Statistics , 38 : 1456 – 1465 .
  • Friedman , J. H. and Stuetzle , W. 1982 . “Smoothing of Scatterplots” , Stanford University, Dept. of Statistics . Technical Report ORION006
  • Gasser , T. and Rosenblatt , M. 1979 . “Smoothing Techniques for Curve Estimation” . In Lecture Notes in Mathematics , New York : Springer-Verlag . No. 757
  • Gebelein , H. 1947 . “Das Statitistiche Problem der Korrelation als Variations und Eigenwert Problem und Sein Zusammenhang mit der Ausgleichung-Srechnung” . Zeitschrift Fuer Angewandte Mathematik und Mechanik , 21 : 364 – 379 .
  • Harrison , D. and Rubinfeld , D. L. 1978 . “Hedonic Housing Prices and the Demand for Clean Air” . Journal of Environmental Economics Management , 5 : 81 – 102 .
  • Kendall , M. A. and Stuart , A. 1967 . The Advanced Theory of Statistics , Vol. 2 , New York : Hafner Publishing .
  • Kimeldorf , G. , May , J. H. and Sampson , A. R. 1982 . “Concordant and Discordant Monotone Correlations and Their Evaluations by Nonlinear Optimization” . In Studies in the Management Sciences (19): Optimization in Statistics , Edited by: Zanakis , S. H. and Rustagi , J. S. 117 – 130 . Amsterdam : North-Holland .
  • Kruskal , J. B. 1964 . “Nonmetric Multidimensional Scaling: A Numerical Method” . Psychometrika , 29 : 115 – 129 .
  • Kruskal , J. B. 1965 . “Analysis of Factorial Experiments by Estimating Monotone Transformations of the Data” . Journal of the Royal Statistical Society , 27 : 251 – 263 . Ser. B
  • Lancaster , H. O. 1958 . “The Structure of Bivariate Distributions” . Annals of Mathematical Statistics , 29 : 719 – 736 .
  • Lancaster , H. O. 1969 . The Chi-Squared Distribution , New York : John Wiley .
  • Linsey , J. K. 1972 . “Fitting Response Surfaces With Power Transformations” . Journal of the Royal Statistical Society , 21 : 234 – 237 . Ser. C
  • Linsey , J. K. 1974 . “Construction and Comparison of Statistical Models” . Journal of the Royal Statistical Society , 36 : 418 – 425 . Ser. B
  • Mosteller , F. and Tukey , J. W. 1977 . Data Analysis and Regression , Reading , MA : Addison-Wesley .
  • Renyi , A. 1959 . “On Measures of Dependence” . Acta Mathematica Academiae Scientiarum Hungaricae , 10 : 441 – 451 .
  • Sarmanov , O. V. 1958a . “The Maximal Correlation Coefficient (Symmetric Case)” . Doklady Akademii Nauk UzSSR , 120 : 715 – 718 .
  • Sarmanov , O. V. 1958b . “The Maximal Correlation Coefficient (Nonsymmetric Case)” . Doklady Akademii Nauk UzSSR , 121 : 52 – 55 .
  • Sarmanov , O. V. and Zaharov , V. K. 1960 . “Maximum Coefficients of Multiple Correlation” . Doklady Akademii Nauk UzSSR , 130 : 269 – 271 .
  • Spiegelman , C. and Sacks , J. 1980 . “Consistent Window Estimation in Nonparametric Regression” . The Annals of Statistics , 8 : 240 – 246 .
  • Stone , C. J. 1977 . “Consistent Nonparametric Regression” . The Annals of Statistics , 7 : 139 – 149 .
  • Tukey , J. W. 1982 . “The Use of Smelting in Guiding Re-Expression” . In Modern Data Analysis , Edited by: Laurner , J. and Siegel , A. New York : Academic Press .
  • Wood , J. T. 1974 . “An Extension of the Analysis of Transformations of Box and Cox” . Journal of the Royal Statistical Society , 23 : 278 – 283 . Ser. C
  • Young , F. W. , de Leeuw , J. and Takane , Y. 1976 . “Regression With Qualitative and Quantitative Variables: An Alternating Least Squares Method With Optimal Scaling Features” . Psychometrika , 41 : 505 – 529 .

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