IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2024i1p15-d1551838.html
   My bibliography  Save this article

New Stochastic Restricted Biased Regression Estimators

Author

Listed:
  • Issam Dawoud

    (Department of Mathematics, Al-Aqsa University, Gaza 4051, Palestine)

  • Hussein Eledum

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia)

Abstract

In this paper, we propose three stochastic restricted biased estimators for the linear regression model. These new estimators generalize the least squares estimator, mixed estimator, and biased estimator. We derive the necessary and sufficient conditions for the superiority of the proposed estimators over existing ones, as well as their relative superiority among each other, using the mean squared error matrix as a criterion. A simulation study is conducted to validate the theoretical findings, and two real-world examples are provided to demonstrate the practical advantages of the proposed estimators.

Suggested Citation

  • Issam Dawoud & Hussein Eledum, 2024. "New Stochastic Restricted Biased Regression Estimators," Mathematics, MDPI, vol. 13(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:15-:d:1551838
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/1/15/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/1/15/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hu Yang & Jianwen Xu, 2009. "An alternative stochastic restricted Liu estimator in linear regression," Statistical Papers, Springer, vol. 50(3), pages 639-647, June.
    2. Jibo Wu & Chaolin Liu, 2014. "Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, April.
    3. Groß, Jürgen, 2003. "Restricted ridge estimation," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 57-64, October.
    4. Yalian Li & Hu Yang, 2016. "More on the two-parameter estimation in the restricted regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7184-7196, December.
    5. Issam Dawoud & B. M. Golam Kibria, 2020. "A New Biased Estimator to Combat the Multicollinearity of the Gaussian Linear Regression Model," Stats, MDPI, vol. 3(4), pages 1-16, November.
    6. M. Hubert & P. Wijekoon, 2006. "Improvement of the Liu estimator in linear regression model," Statistical Papers, Springer, vol. 47(3), pages 471-479, June.
    Full references (including those not matched with items on IDEAS)

    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. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    2. Murat Genç, 2022. "A new double-regularized regression using Liu and lasso regularization," Computational Statistics, Springer, vol. 37(1), pages 159-227, March.
    3. Autcha Araveeporn, 2024. "Modified Liu Parameters for Scaling Options of the Multiple Regression Model with Multicollinearity Problem," Mathematics, MDPI, vol. 12(19), pages 1-18, October.
    4. Yalian Li & Hu Yang, 2010. "A new stochastic mixed ridge estimator in linear regression model," Statistical Papers, Springer, vol. 51(2), pages 315-323, June.
    5. Yalian Li & Hu Yang, 2019. "Performance of the restricted almost unbiased type principal components estimators in linear regression model," Statistical Papers, Springer, vol. 60(1), pages 19-34, February.
    6. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    7. M. Revan Özkale, 2014. "The relative efficiency of the restricted estimators in linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 998-1027, May.
    8. 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.
    9. Jahufer, Aboobacker & Jianbao, Chen, 2009. "Assessing global influential observations in modified ridge regression," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 513-518, February.
    10. 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.
    11. Esra Akdeniz Duran & Fikri Akdeniz, 2012. "Efficiency of the modified jackknifed Liu-type estimator," Statistical Papers, Springer, vol. 53(2), pages 265-280, May.
    12. Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
    13. M. Revan Özkale & Atif Abbasi, 2022. "Iterative restricted OK estimator in generalized linear models and the selection of tuning parameters via MSE and genetic algorithm," Statistical Papers, Springer, vol. 63(6), pages 1979-2040, December.
    14. M. Alkhamisi, 2010. "Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies," Statistical Papers, Springer, vol. 51(3), pages 651-672, September.
    15. Ning Li & Hu Yang, 2021. "Nonnegative estimation and variable selection under minimax concave penalty for sparse high-dimensional linear regression models," Statistical Papers, Springer, vol. 62(2), pages 661-680, April.
    16. Bahadır Yüzbaşı & S. Ejaz Ahmed, 2020. "Ridge Type Shrinkage Estimation of Seemingly Unrelated Regressions And Analytics of Economic and Financial Data from “Fragile Five” Countries," JRFM, MDPI, vol. 13(6), pages 1-19, June.
    17. M. Revan Özkale & Hans Nyquist, 2021. "The stochastic restricted ridge estimator in generalized linear models," Statistical Papers, Springer, vol. 62(3), pages 1421-1460, June.
    18. Aboobacker Jahufer & Jianbao Chen, 2012. "Identifying local influential observations in Liu estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 425-438, April.
    19. Özkale, M. Revan, 2009. "A stochastic restricted ridge regression estimator," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1706-1716, September.
    20. Hu Yang & Jianwen Xu, 2011. "Preliminary test Liu estimators based on the conflicting W, LR and LM tests in a regression model with multivariate Student-t error," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 275-292, May.

    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:13:y:2024:i:1:p:15-:d:1551838. 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.