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Some Modified Ridge Estimators for Handling the Multicollinearity Problem

Author

Listed:
  • Nusrat Shaheen

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

  • Ismail Shah

    (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.)

  • Sajid Ali

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

  • Hana N. Alqifari

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

Abstract

Regression analysis is a statistical process that utilizes two or more predictor variables to predict a response variable. When the predictors included in the regression model are strongly correlated with each other, the problem of multicollinearity arises in the model. Due to this problem, the model variance increases significantly, leading to inconsistent ordinary least-squares estimators that may lead to invalid inferences. There are numerous existing strategies used to solve the multicollinearity issue, and one of the most used methods is ridge regression. The aim of this work is to develop novel estimators for the ridge parameter “ γ ” and compare them with existing estimators via extensive Monte Carlo simulation and real data sets based on the mean squared error criterion. The study findings indicate that the proposed estimators outperform the existing estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2522-:d:1160223
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    References listed on IDEAS

    as
    1. Ka Wong & Sung Chiu, 2015. "An iterative approach to minimize the mean squared error in ridge regression," Computational Statistics, Springer, vol. 30(2), pages 625-639, June.
    2. 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.
    3. M. Arashi & T. Valizadeh, 2015. "Performance of Kibria’s methods in partial linear ridge regression model," Statistical Papers, Springer, vol. 56(1), pages 231-246, February.
    4. 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.
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    Cited by:

    1. Salomi du Plessis & Mohammad Arashi & Gaonyalelwe Maribe & Salomon M. Millard, 2023. "Efficient Estimation and Validation of Shrinkage Estimators in Big Data Analytics," Mathematics, MDPI, vol. 11(22), pages 1-11, November.

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