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Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion

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  • Roozbeh, Mahdi

Abstract

Multicollinearity among the predictor variables is a serious problem in regression analysis. There are some classes of biased estimators for solving the problem in statistical literature. In these biased classes, estimation of the shrinkage parameter plays an important role in data analyzing. Using eigenvalue analysis, efforts have been made to develop skills and methods for computing risk function of the estimators in regression models. A modified estimator based on the QR decomposition to combat the multicollinearity problem of design matrix is proposed in partially linear regression model which makes the data to be less distorted than the other methods. The necessary and sufficient condition for the superiority of the partially generalized QR-based estimator over partially generalized least-squares estimator for selecting the shrinkage parameter is obtained. Under appropriate assumptions, the asymptotic bias and variance of the proposed estimators are obtained. Also, a generalized cross validation (GCV) criterion is proposed for selecting the optimal shrinkage parameter and the bandwidth of the kernel smoother and then, an extension of the GCV theorem is established to prove the convergence of the GCV mean. Finally, the Monté-Carlo simulation studies and a real application related to electricity consumption data are conducted to support our theoretical discussion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:45-61
    DOI: 10.1016/j.csda.2017.08.002
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    References listed on IDEAS

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    1. Roozbeh, Mahdi, 2015. "Shrinkage ridge estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 56-74.
    2. M. Arashi & M. Janfada & M. Norouzirad, 2015. "Singular Ridge Regression With Stochastic Constraints," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(6), pages 1281-1292, March.
    3. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    4. 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.
    5. 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.
    6. You, Jinhong & Chen, Gemai & Zhou, Yong, 2007. "Statistical inference of partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1539-1557, September.
    7. Jialiang Li & Wenyang Zhang & Zhengxiao Wu, 2011. "Optimal zone for bandwidth selection in semiparametric models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 701-717.
    8. Sarkar, Nityananda, 1996. "Mean square error matrix comparison of some estimators in linear regressions with multicollinearity," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 133-138, October.
    9. 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.
    10. Esra Akdeniz Duran & Fikri Akdeniz, 2012. "Efficiency of the modified jackknifed Liu-type estimator," Statistical Papers, Springer, vol. 53(2), pages 265-280, May.
    11. 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.
    12. Miller, D. & Golan, Amos & Judge, G., 1998. "Information Recovery in Simultaneous Equation Statistical Models," Staff General Research Papers Archive 1319, Iowa State University, Department of Economics.
    13. Roozbeh, M. & Arashi, M., 2013. "Feasible ridge estimator in partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 35-44.
    14. M. Hubert & P. Wijekoon, 2006. "Improvement of the Liu estimator in linear regression model," Statistical Papers, Springer, vol. 47(3), pages 471-479, June.
    15. repec:hum:journl:v:105:y:2012:i:1:p:164-175 is not listed on IDEAS
    16. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
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    Cited by:

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    3. 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.
    4. Julio C. S. Vasconcelos & Denize P. dos Santos & Fernando J. B. Brandão & Edwin M. M. Ortega & Marco A. M. Biaggioni & Gauss M. Cordeiro, 2024. "Spiral polyethylene tube solar collectors performance analyzed by a new partially linear regression model," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 26(2), pages 5401-5417, February.
    5. Guoping Zeng & Sha Tao, 2023. "A Generalized Linear Transformation and Its Effects on Logistic Regression," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    6. Laura Vicente-Gonzalez & Elisa Frutos-Bernal & Jose Luis Vicente-Villardon, 2025. "Partial Least Squares Regression for Binary Data," Mathematics, MDPI, vol. 13(3), pages 1-29, January.
    7. Lei Qiao & Bing Wang, 2024. "Kernel-Based Multivariate Nonparametric CUSUM Multi-Chart for Detection of Abrupt Changes," Mathematics, MDPI, vol. 12(10), pages 1-12, May.

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