IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i11p2522-d1160223.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/11/2522/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/11/2522/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    2. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    3. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    4. 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.
    5. Sivarajah Arumairajan & Pushpakanthie Wijekoon, 2017. "The generalized preliminary test estimator when different sets of stochastic restrictions are available," Statistical Papers, Springer, vol. 58(3), pages 729-747, September.
    6. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    7. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    8. Hongchang Hu & Yu Zhang & Xiong Pan, 2016. "Asymptotic normality of DHD estimators in a partially linear model," Statistical Papers, Springer, vol. 57(3), pages 567-587, September.
    9. Waleed B. Altukhaes & Mahdi Roozbeh & Nur A. Mohamed, 2024. "Robust Liu Estimator Used to Combat Some Challenges in Partially Linear Regression Model by Improving LTS Algorithm Using Semidefinite Programming," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    10. Bahadır Yüzbaşı & S. Ejaz Ahmed & Dursun Aydın, 2020. "Ridge-type pretest and shrinkage estimations in partially linear models," Statistical Papers, Springer, vol. 61(2), pages 869-898, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2522-:d:1160223. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.