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The VIF and MSE in Raise Regression

Author

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  • Román Salmerón Gómez

    (Department of Quantitative Methods for Economics and Business, University of Granada, 18010 Granada, Spain)

  • Ainara Rodríguez Sánchez

    (Department of Economic Theory and History, University of Granada, 18010 Granada, Spain)

  • Catalina García García

    (Department of Quantitative Methods for Economics and Business, University of Granada, 18010 Granada, Spain)

  • José García Pérez

    (Department of Economy and Company, University of Almería, 04120 Almería, Spain)

Abstract

The raise regression has been proposed as an alternative to ordinary least squares estimation when a model presents collinearity. In order to analyze whether the problem has been mitigated, it is necessary to develop measures to detect collinearity after the application of the raise regression. This paper extends the concept of the variance inflation factor to be applied in a raise regression. The relevance of this extension is that it can be applied to determine the raising factor which allows an optimal application of this technique. The mean square error is also calculated since the raise regression provides a biased estimator. The results are illustrated by two empirical examples where the application of the raise estimator is compared to the application of the ridge and Lasso estimators that are commonly applied to estimate models with multicollinearity as an alternative to ordinary least squares.

Suggested Citation

  • Román Salmerón Gómez & Ainara Rodríguez Sánchez & Catalina García García & José García Pérez, 2020. "The VIF and MSE in Raise Regression," Mathematics, MDPI, vol. 8(4), pages 1-28, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:605-:d:346167
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    References listed on IDEAS

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    1. Yoshimasa Uematsu & Shinya Tanaka, 2019. "High‐dimensional macroeconomic forecasting and variable selection via penalized regression," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 34-56.
    2. Artur Klinger, 2001. "Inference in high dimensional generalized linear models based on soft thresholding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 377-392.
    3. Kazuhiro Ohtani, 1998. "An MSE comparison of the restricted Stein-rule and minimum mean squared error estimators in regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 361-376, December.
    4. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    5. Catalina Garcia & José Pérez & José Liria, 2011. "The raise method. An alternative procedure to estimate the parameters in presence of collinearity," Quality & Quantity: International Journal of Methodology, Springer, vol. 45(2), pages 403-423, February.
    6. Henk Kiers & Age Smilde, 2007. "A comparison of various methods for multivariate regression with highly collinear variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(2), pages 193-228, August.
    7. Wenxing Guo & Xiaohui Liu & Shangli Zhang, 2016. "The principal correlation components estimator and its optimality," Statistical Papers, Springer, vol. 57(3), pages 755-779, September.
    8. Mia Hubert & Irène Gijbels & Dina Vanpaemel, 2013. "Reducing the mean squared error of quantile-based estimators by smoothing," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 448-465, September.
    9. Yalian Li & Hu Yang, 2012. "A new Liu-type estimator in linear regression model," Statistical Papers, Springer, vol. 53(2), pages 427-437, May.
    10. Golan, Amos, 2008. "Information and Entropy Econometrics — A Review and Synthesis," Foundations and Trends(R) in Econometrics, now publishers, vol. 2(1–2), pages 1-145, February.
    11. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    12. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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