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Kibria–Lukman-Type Estimator for Regularization and Variable Selection with Application to Cancer Data

Author

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  • Adewale Folaranmi Lukman

    (Department of Mathematics, University of North Dakota, Grand Forks, ND 58202, USA)

  • Jeza Allohibi

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

  • Segun Light Jegede

    (Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA)

  • Emmanuel Taiwo Adewuyi

    (Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria)

  • Segun Oke

    (Department of Physics, Chemistry and Mathematics, Alabama A&M University, Huntsville, AL 35762, USA)

  • Abdulmajeed Atiah Alharbi

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

Abstract

Following the idea presented with regard to the elastic-net and Liu-LASSO estimators, we proposed a new penalized estimator based on the Kibria–Lukman estimator with L1-norms to perform both regularization and variable selection. We defined the coordinate descent algorithm for the new estimator and compared its performance with those of some existing machine learning techniques, such as the least absolute shrinkage and selection operator (LASSO), the elastic-net, Liu-LASSO, the GO estimator and the ridge estimator, through simulation studies and real-life applications in terms of test mean squared error (TMSE), coefficient mean squared error (βMSE), false-positive (FP) coefficients and false-negative (FN) coefficients. Our results revealed that the new penalized estimator performs well for both the simulated low- and high-dimensional data in simulations. Also, the two real-life results show that the new method predicts the target variable better than the existing ones using the test RMSE metric.

Suggested Citation

  • Adewale Folaranmi Lukman & Jeza Allohibi & Segun Light Jegede & Emmanuel Taiwo Adewuyi & Segun Oke & Abdulmajeed Atiah Alharbi, 2023. "Kibria–Lukman-Type Estimator for Regularization and Variable Selection with Application to Cancer Data," Mathematics, MDPI, vol. 11(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4795-:d:1289070
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    References listed on IDEAS

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    1. Murat Genç & M. Revan Özkale, 2021. "Usage of the GO estimator in high dimensional linear models," Computational Statistics, Springer, vol. 36(1), pages 217-239, March.
    2. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

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