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Transformation of variables and the condition number in ridge estimation

Author

Listed:
  • Román Salmerón

    (University of Granada)

  • José García

    (University of Almería)

  • Catalina García

    (University of Granada)

  • María del Mar López

    (University of Granada)

Abstract

Ridge estimation (RE) is an alternative method to ordinary least squares (OLS) estimation when collinearity is detected in a linear regression model. After applying RE, it is sensible to determine whether such collinearity has been mitigated. The condition number (CN) is a commonly applied measure to detect the presence of collinearity in econometric models, but to the best of our knowledge, it has not been extended to be applied after RE. In OLS estimation, Belsley et al. (Regression diagnostics: identifying influential data and sources of collinearity, Wiley, New York, 1980) established that the regressors must be of unit length and not centered to correctly calculate the CN. This paper reviews this requirement in the context of RE and presents an expression to calculate the CN in RE.

Suggested Citation

  • Román Salmerón & José García & Catalina García & María del Mar López, 2018. "Transformation of variables and the condition number in ridge estimation," Computational Statistics, Springer, vol. 33(3), pages 1497-1524, September.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:3:d:10.1007_s00180-017-0769-4
    DOI: 10.1007/s00180-017-0769-4
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    References listed on IDEAS

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    1. Alexis Lazaridis, 2007. "A Note Regarding the Condition Number: The Case of Spurious and Latent Multicollinearity," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(1), pages 123-135, February.
    2. Wichers, C Robert, 1975. "The Detection of Multicollinearity: A Comment," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 366-368, August.
    3. Belsley, David A., 1982. "Assessing the presence of harmful collinearity and other forms of weak data through a test for signal-to-noise," Journal of Econometrics, Elsevier, vol. 20(2), pages 211-253, November.
    4. M. Alkhamisi & I. MacNeill, 2015. "Recent results in ridge regression methods," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 359-376, December.
    5. Friendly, Michael & Kwan, Ernest, 2009. "Where's Waldo? Visualizing Collinearity Diagnostics," The American Statistician, American Statistical Association, vol. 63(1), pages 56-65.
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