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Optimal partial ridge estimation in restricted semiparametric regression models

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  • Amini, Morteza
  • Roozbeh, Mahdi

Abstract

This paper is concerned with the ridge estimation of the parameter vector β in partial linear regression model yi=xiβ+f(ti)+ϵi,1≤i≤n, with correlated errors, that is, when Cov(ϵ)=σ2V, with a positive definite matrix V and ϵ=(ϵ1,…,ϵn), under the linear constraint Rβ=r, for a given matrix R and a given vector r. The partial residual estimation method is used to estimate β and the function f(⋅). Under appropriate assumptions, the asymptotic bias and variance of the proposed estimators are obtained. A generalized cross validation (GCV) criterion is proposed for selecting the optimal ridge parameter and the bandwidth of the kernel smoother. An extension of the GCV theorem is established to prove the convergence of the GCV mean. The theoretical results are illustrated by a real data example and a simulation study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:136:y:2015:i:c:p:26-40
    DOI: 10.1016/j.jmva.2015.01.005
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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.
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    Cited by:

    1. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    2. M Arashi & M Roozbeh & N A Hamzah & M Gasparini, 2021. "Ridge regression and its applications in genetic studies," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-17, April.
    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. Guoping Zeng & Sha Tao, 2023. "A Generalized Linear Transformation and Its Effects on Logistic Regression," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    5. 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.
    6. 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.
    7. M. Nooi Asl & H. Bevrani & R. Arabi Belaghi & K. Mansson, 2021. "Ridge-type shrinkage estimators in generalized linear models with an application to prostate cancer data," Statistical Papers, Springer, vol. 62(2), pages 1043-1085, April.
    8. 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.
    9. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    10. 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.
    11. Morteza Amini & Mahdi Roozbeh, 2019. "Improving the prediction performance of the LASSO by subtracting the additive structural noises," Computational Statistics, Springer, vol. 34(1), pages 415-432, March.

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