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Robust ridge and robust Liu estimator for regression based on the LTS estimator

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  • Betül Kan
  • Özlem Alpu
  • Berna Yazıcı

Abstract

In the multiple linear regression analysis, the ridge regression estimator and the Liu estimator are often used to address multicollinearity. Besides multicollinearity, outliers are also a problem in the multiple linear regression analysis. We propose new biased estimators based on the least trimmed squares (LTS) ridge estimator and the LTS Liu estimator in the case of the presence of both outliers and multicollinearity. For this purpose, a simulation study is conducted in order to see the difference between the robust ridge estimator and the robust Liu estimator in terms of their effectiveness; the mean square error. In our simulations, the behavior of the new biased estimators is examined for types of outliers: X-space outlier, Y-space outlier, and X-and Y-space outlier. The results for a number of different illustrative cases are presented. This paper also provides the results for the robust ridge regression and robust Liu estimators based on a real-life data set combining the problem of multicollinearity and outliers.

Suggested Citation

  • Betül Kan & Özlem Alpu & Berna Yazıcı, 2013. "Robust ridge and robust Liu estimator for regression based on the LTS estimator," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(3), pages 644-655.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:3:p:644-655
    DOI: 10.1080/02664763.2012.750285
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    Cited by:

    1. M. Norouzirad & M. Arashi, 2019. "Preliminary test and Stein-type shrinkage ridge estimators in robust regression," Statistical Papers, Springer, vol. 60(6), pages 1849-1882, December.
    2. Issam Dawoud & B. M. Golam Kibria, 2020. "A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model," Stats, MDPI, vol. 3(4), pages 1-16, November.

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