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Feasible ridge estimator in partially linear models

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  • Roozbeh, M.
  • Arashi, M.

Abstract

In a partial linear model, some non-stochastic linear restrictions are imposed under a multicollinearity setting. Semiparametric ridge and non-ridge type estimators, in a restricted manifold are defined. For practical use, it is assumed that the covariance matrix of the error term is unknown and thus feasible estimators are replaced and their asymptotic distributional properties are derived. Also, necessary and sufficient conditions, for the superiority of the ridge type estimator over its counterpart, for selecting the ridge parameter k are obtained. Lastly, a Monte Carlo simulation study is conducted to estimate the parametric and non-parametric parts. In this regard, kernel smoothing and cross validation methods for estimating the non-parametric function are used.

Suggested Citation

  • Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:35-44
    DOI: 10.1016/j.jmva.2012.11.006
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    References listed on IDEAS

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    1. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    2. 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.
    3. 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.
    4. Groß, Jürgen, 2003. "Restricted ridge estimation," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 57-64, October.
    5. B. M. Golam Kibria & A. K. Md. E. Saleh, 2004. "Preliminary test ridge regression estimators with student’s t errors and conflicting test-statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 105-124, May.
    6. repec:hum:journl:v:105:y:2012:i:1:p:164-175 is not listed on IDEAS
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    Citations

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    Cited by:

    1. 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.
    2. Jing Li & Xueyan Li, 2019. "Liu Estimator in Semiparametric Partially Linear Varying Coefficient Models," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-69, November.
    3. 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.
    4. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    5. Sergio Perez-Melo & B. M. Golam Kibria, 2020. "On Some Test Statistics for Testing the Regression Coefficients in Presence of Multicollinearity: A Simulation Study," Stats, MDPI, vol. 3(1), pages 1-16, March.
    6. 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.
    7. Mohammad Arashi & Mahdi Roozbeh, 2015. "Shrinkage estimation in system regression model," Computational Statistics, Springer, vol. 30(2), pages 359-376, June.
    8. 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.
    9. 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.
    10. Hadi Emami & Omid Khademnoe, 2025. "Shrinkage and pretest Liu estimators in semiparametric linear measurement error models," Statistical Papers, Springer, vol. 66(2), pages 1-35, February.
    11. Chuanhua Wei & Xiaonan Wang, 2016. "Liu-type estimator in semiparametric partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 459-468, September.
    12. Mohammad Arashi & Mina Norouzirad & S. Ejaz Ahmed & Bahadır Yüzbaşı, 2018. "Rank-based Liu regression," Computational Statistics, Springer, vol. 33(3), pages 1525-1561, September.
    13. Amini, Morteza & Roozbeh, Mahdi, 2015. "Optimal partial ridge estimation in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 26-40.
    14. J. Kleyn & M. Arashi & S. Millard, 2018. "Preliminary test estimation in system regression models in view of asymmetry," Computational Statistics, Springer, vol. 33(4), pages 1897-1921, December.
    15. Zhao, Yan-Yong & Zhang, Yuchun & Liu, Yuan & Ismail, Noriszura, 2024. "Distributed debiased estimation of high-dimensional partially linear models with jumps," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).

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