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A New Quantile-Based Approach for LASSO Estimation

Author

Listed:
  • Ismail Shah

    (Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    These authors contributed equally to this work.)

  • Hina Naz

    (Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    These authors contributed equally to this work.)

  • Sajid Ali

    (Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    These authors contributed equally to this work.)

  • Amani Almohaimeed

    (Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
    These authors contributed equally to this work.)

  • Showkat Ahmad Lone

    (Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

Regularization regression techniques are widely used to overcome a model’s parameter estimation problem in the presence of multicollinearity. Several biased techniques are available in the literature, including ridge, Least Angle Shrinkage Selection Operator (LASSO), and elastic net. In this work, we study the performance of the classical LASSO, adaptive LASSO, and ordinary least squares (OLS) methods in high-multicollinearity scenarios and propose some new estimators for estimating the LASSO parameter “k”. The performance of the proposed estimators is evaluated using extensive Monte Carlo simulations and real-life examples. Based on the mean square error criterion, the results suggest that the proposed estimators outperformed the existing estimators.

Suggested Citation

  • Ismail Shah & Hina Naz & Sajid Ali & Amani Almohaimeed & Showkat Ahmad Lone, 2023. "A New Quantile-Based Approach for LASSO Estimation," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1452-:d:1099653
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    References listed on IDEAS

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    Cited by:

    1. Nusrat Shaheen & Ismail Shah & Amani Almohaimeed & Sajid Ali & Hana N. Alqifari, 2023. "Some Modified Ridge Estimators for Handling the Multicollinearity Problem," Mathematics, MDPI, vol. 11(11), pages 1-19, May.

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