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Preliminary test and Stein-type shrinkage ridge estimators in robust regression

Author

Listed:
  • M. Norouzirad

    (Shahrood University of Technology)

  • M. Arashi

    (Shahrood University of Technology)

Abstract

A statistician may face with a dataset that suffers from multicollinearity and outliers, simultaneously. The Huberized ridge (HR) estimator is a technique that can be used here. On the other hand, an expert may claim that some/all the variables should be removed from the analysis, due to inappropriateness, that imposes a prior information that all coefficients equal to zero (in the form of a restriction) to the analysis. In such situations, one may consider the HR estimation under the subspace restriction. In this paper, we introduce some improved estimators for verifying this claim. They are employed to improve the performance of the HR estimator in the multiple regression model. Advantages of the proposed estimators over the usual HR estimator are demonstrated through a Monte Carlo simulation as well as two real data examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:6:d:10.1007_s00362-017-0899-3
    DOI: 10.1007/s00362-017-0899-3
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    References listed on IDEAS

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    1. Gülin Tabakan & Fikri Akdeniz, 2010. "Difference-based ridge estimator of parameters in partial linear model," Statistical Papers, Springer, vol. 51(2), pages 357-368, June.
    2. Olcay Arslan & Nedret Billor, 2000. "Robust Liu estimator for regression based on an M-estimator," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(1), pages 39-47.
    3. 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.
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    Citations

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    Cited by:

    1. Hirofumi Michimae & Takeshi Emura, 2022. "Bayesian ridge estimators based on copula-based joint prior distributions for regression coefficients," Computational Statistics, Springer, vol. 37(5), pages 2741-2769, November.
    2. Jan Pablo Burgard & Joscha Krause & Dennis Kreber & Domingo Morales, 2021. "The generalized equivalence of regularization and min–max robustification in linear mixed models," Statistical Papers, Springer, vol. 62(6), pages 2857-2883, December.
    3. Sergio Perez-Melo & B. M. Golam Kibria, 2020. "On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study," Stats, MDPI, vol. 3(1), pages 1-16, March.

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