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Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models

Author

Listed:
  • Fikri Akdeniz

    (Çağ University)

  • Mahdi Roozbeh

    (Semnan University)

Abstract

In this paper, a generalized difference-based estimator is introduced for the vector parameter $$\beta $$ β in partially linear model when the errors are correlated. A generalized difference-based almost unbiased ridge estimator is defined for the vector parameter $$\beta $$ β . Under the linear stochastic constraint $$r=R\beta +e$$ r = R β + e , a new generalized difference-based weighted mixed almost unbiased ridge estimator is proposed. The performance of this estimator over the generalized difference-based weighted mixed estimator, the generalized difference-based estimator, and the generalized difference-based almost unbiased ridge estimator in terms of the mean square error matrix criterion is investigated. Then, a method to select the biasing parameter k and non-stochastic weight $$\omega $$ ω is considered. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.

Suggested Citation

  • Fikri Akdeniz & Mahdi Roozbeh, 2019. "Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models," Statistical Papers, Springer, vol. 60(5), pages 1717-1739, October.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0893-9
    DOI: 10.1007/s00362-017-0893-9
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    References listed on IDEAS

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    1. Helge Toutenburg & Viren K. Srivastava & Burkhard Schaffrin & Christian Heumann, 2003. "Efficiency properties of weighted mixed regression estimation," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 91-103.
    2. Sivarajah Arumairajan & Pushpakanthie Wijekoon, 2014. "Improvement of Ridge Estimator When Stochastic Restrictions Are Available in the Linear Regression Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 3(1), pages 1-3.
    3. Gülin Tabakan & Fikri Akdeniz, 2010. "Difference-based ridge estimator of parameters in partial linear model," Statistical Papers, Springer, vol. 51(2), pages 357-368, June.
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    5. 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.
    6. 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.
    7. Yatchew,Adonis, 2003. "Semiparametric Regression for the Applied Econometrician," Cambridge Books, Cambridge University Press, number 9780521012263, January.
    8. Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
    9. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
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    Cited by:

    1. Mohammad Arashi & Mina Norouzirad & Mahdi Roozbeh & Naushad Mamode Khan, 2021. "A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    2. 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.

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