Shifted Liu-Type Estimator in The Linear Regression
DOI:
https://doi.org/10.20956/j.v19i1.21136Keywords:
Multicollinearity, Biased estimation, Ridge estimator, Liu estimatorAbstract
The methods to solve the problem of multicollinearity have an important issue in the linear regression. The Liu-type estimator is one of these methods used to reduce its effect. This estimator is an estimator with two parameters denoted and . Kurnaz and Akay (2015) [6] introduced a new approach for the Liu-type estimator and called it new Liu-type (NL) estimator. This proposed estimator is based on a continuous function of rather than two parameters and includes OLS, ridge estimator, Liu estimator, and some estimators with two biasing parameters as special cases. This study aimed to improve the NL estimator by shifting. The performance of the shifted NL estimator is compared to the NL estimator and other estimators depending on the mean squared error (MSE) criterion. The real data example and simulation study reveal that the SNL estimator can be a good selection in the linear regression model.Downloads
References
Guilkey D.K. & Murphy J.L., 1975. Directed Ridge Regression Techniques in Cases of Multicollinearity. Journal of the American Statistical Association, Vol. 70, No. 352, 769 – 775.
Gunst R.F. & Mason R.L., 1977. Biased Estimation in Regression: An Evaluation Using Mean Squared Error. Journal of the American Statistical Association, Vol. 72, No. 359, 616 – 628.
Hoerl A.E. & Kennard R.W., 1970a. Ridge Regression: Biased Estimation for Nonorthogonal Problems. Technometrics, Vol. 12, No. 1, 55 – 67.
Hoerl A.E. & Kennard R.W., 1970b. Ridge Regression: Application to Non-Orthogonal Problems. Technometrics, Vol. 12, 69 – 82.
Hoerl A.E., Kennard R.W. & Baldwin K.F., 1975. Ridge Regression: Some Simulations. Communications in Statistics – Simulation and Computation, Vol. 4, 105 – 123.
Kurnaz F.S. & Akay K.U., 2015. A New Liu-Type Estimator. Statistical Papers, Vol. 56, No. 2, 495 – 517.
Liu K., 1993. A New Class of Biased Estimate in Linear Regression. Communications in Statistics - Theory and Methods, Vol. 22, No. 2, 393 – 402.
Liu K., 2003. Using Liu-Type Estimator to Combat Collinearity. Communications in Statistics - Theory and Methods Vol. 32, 1009 – 1020.
McDonald G.C. & Galarneau D.I., 1975. A Monte Carlo Evaluation of Some Ridge-Type Estimators. J Am Stat Assoc, Vol. 70, 407 – 416.
Özkale M.R. & Kaçiranlar S., 2007. The Restricted and Unrestricted Two-Parameter Estimators. Communications in Statistics - Theory and Methods, Vol. 36, 2707 – 2725.
Sakallıoğlu S. & Kaçıranlar S., 2008. A New Biased Estimator Based on Ridge Estimation. Statistical Papers, Vol. 49, 669 – 689.
Stein C., 1956. Inadmissibility of The Usual Estimator for Mean of Multivariate Normal Distribution. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, 197 – 206.
Trenkler G. & Toutenburg H., 1990. Mean Squared Error Matrix Comparisons Between Biased Estimators: An Overview of Recent Results. Statistical Papers, Vol. 31, 165 – 179.
Vinod H.D., 1978. A Survey of Ridge Regression and Related Techniques for Improvements Over Ordinary Least Squares. The Review of Economics and Statistics, 121 – 131.
Woods H, Stenior H.H. & Starke H.R., 1932. Effect of Composition of Portland Cement on Heat Evolved During Hardening. Ind Eng Chem, Vol. 24, 1207 – 1214.
Yang H. & Chang X., 2010. A New Two-Parameter Estimator in Linear Regression. Communications in Statistics - Theory and Methods, Vol. 39, No. 6, 923 – 934.
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This work is licensed under a Creative Commons Attribution 4.0 International License.
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