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Restricted ridge estimation

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  • Groß, Jürgen

Abstract

In this paper, we introduce a ridge estimator for the vector of parameters in a linear regression model when additional linear restrictions on the parameter vector are assumed to hold. The estimator is a generalization of the well-known restricted least-squares estimator and is confined to the (affine) subspace which is generated by the restrictions. Necessary and sufficient conditions for the superiority of the new estimator over the restricted least-squares estimator are derived. Our new estimator is not to be confounded with the restricted ridge regression estimator introduced by Sarkar (Comm. Statist. Theory Methods 21 (1992) 1987).

Suggested Citation

  • Groß, Jürgen, 2003. "Restricted ridge estimation," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 57-64, October.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:1:p:57-64
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    7. Jahufer, Aboobacker & Jianbao, Chen, 2009. "Assessing global influential observations in modified ridge regression," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 513-518, February.
    8. 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.
    9. Jianwen Xu & Hu Yang, 2011. "On the restricted almost unbiased estimators in linear regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 605-617, November.
    10. M. Alkhamisi & I. MacNeill, 2015. "Recent results in ridge regression methods," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 359-376, December.
    11. 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.
    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. Özkale, M. Revan, 2009. "A stochastic restricted ridge regression estimator," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1706-1716, September.
    14. 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.

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