Collinearity and Alternative Estimates

Part of the Springer Texts in Statistics book series (STS)


This chapter deals with problems caused by having predictor variables that are very nearly redundant. It examines estimation methods developed for dealing with those problems and then goes on to introduce a variety of alternatives to least squares estimation including robust and penalized (regularized) estimates. Penalized estimation is discussed in more detail in ALM-III.


  1. Belsley, D. A. (1984). Demeaning conditioning diagnostics through centering (with discussion). The American Statistician, 38, 73–77.Google Scholar
  2. Belsley, D. A. (1991). Collinearity diagnostics: Collinearity and weak data in regression. New York: Wiley.zbMATHGoogle Scholar
  3. Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. New York: Wiley.CrossRefGoogle Scholar
  4. Christensen, R. (2015). Analysis of variance, design, and regression: Linear modeling for unbalanced data (2nd ed.). Boca Raton, FL: Chapman and Hall/CRC Press.Google Scholar
  5. Christensen, R. (2018). Comment on “A note on collinearity diagnostics and centering” by Velilla (2018). The American Statistician, 72, 114–117.CrossRefGoogle Scholar
  6. Draper, N. R., & van Nostrand, R. C. (1979). Ridge regression and James-Stein estimation: Review and comments. Technometrics, 21, 451–466.MathSciNetCrossRefGoogle Scholar
  7. Goldstein, M., & Smith, A. F. M. (1974). Ridge-type estimators for regression analysis. Journal of the Royal Statistical Society, Series B, 26, 284–291.MathSciNetzbMATHGoogle Scholar
  8. Hoerl, A. E., & Kennard, R. (1970). Ridge regression: Biased estimation for non-orthogonal problems. Technometrics, 12, 55–67.CrossRefGoogle Scholar
  9. Huber, P. J., & Ronchetti, E. M. (2009). Robust statistics (2nd ed.). New York: Wiley.CrossRefGoogle Scholar
  10. Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed.). Englewood Cliffs, NJ: Prentice-Hall.zbMATHGoogle Scholar
  11. Marquardt, D. W. (1970). Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics, 12, 591–612.CrossRefGoogle Scholar
  12. Moguerza, J. M., & Muñoz, A. (2006). Support vector machines with applications. Statistical Science, 21, 322–336.MathSciNetCrossRefGoogle Scholar
  13. Mosteller, F., & Tukey, J. W. (1977). Data analysis and regression. Reading, MA: Addison-Wesley.Google Scholar
  14. Velilla, S. (2018). A note on collinearity diagnostics and centering. The American Statistician, 72, 140–146.MathSciNetCrossRefGoogle Scholar
  15. Zhu, M. (2008). Kernels and ensembles: Perspectives on statistical learning. The American Statistician, 62, 97–109.MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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