On Restricted Shrinkage Jackknife Biased Estimator for Restricted Linear Regression Model

Mohammed, Ahmed A.; Algareri, Feras Shaker

doi:10.37652/juaps.2023.181574

Document Type : Research Paper

Authors

¹ Department of Mathematics, College of Education for Pure Science, University of Anbar, Anbar, Iraq;

² Anbar University, College of Education for Pure Sciences, Department of Mathematics.

https://doi.org/10.37652/juaps.2023.181574

Abstract

In restricted linear regression model, more methods proposed to address the Multicollinearity problem and the high variance. For example, shrinkage biased estimation and optimization (Lagrange function). In this paper, we propose new biased estimator based on philosophy of Jackknife with the restricted least squares estimator. A new estimator called Restricted Shrinkage Jackknife estimator (RSJ). Also, we show that the statistical properties of new estimator with some theorems to compare the performance of new estimator with some restricted estimators and we make simulation study of these estimators. Finally, a real data has been taken into consideration to demonstrate how well the estimators perform.

Keywords

Main Subjects

Mathematical

References

Wooldridge, J. M. 2020. Introductory Econometrics: A Modern Approach. 7^th Edition, Cengage Learning, Boston, USA.

Sarkar, N., 1992. A new estimator combining the ridge regression and the restricted least squares methods of estimation. Commun. Stat. Theory Methods21: 1987–2000.

Özkale, M. R., and Kaciranlar. S. (2007). The restricted and unrestricted two-parameter estimators. Communications in Statistics—Theory and Methods, 36: 2707-2725.

Yang, H. and Xu, J.W. (2009) An alternative stochastic restricted Liu estimator in linear regression, Statist. Papers 50, 639 – 647

Xu, G.X. and Yang, J.Z. (2011) Building and Application of PCA-GA-SVM Model-Empirical Analysis of Prediction Accuracy of Shanghai and Shenzhen Index. Quantitative & Technical Economics, 2, 135 – 147.

Huang, H., Wu, J & Yi, W. (2016). On the restricted almost unbiased two-parameter estimator in linear regression model, Communications in Statistics- Theory and Methods, 46(4): 1668 – 1678.

Mohammed, B .A and ALheety, M .I. (2023). New shrinkage restricted estimator for restricted linear regression model. AIP Conference Proceedings 2414, 040044.

Gülesen Üstündağ Şiray, Selma Toker, Nimet Özbay. (2021) Defining a two-parameter estimator: a mathematical programming evidence. Journal of Statistical Computation and Simulation 91(11): 2133 – 2152.

Batah F, Ramanathan TK, and Gore S. D. 2008. The efficiency of modified jackknife and ridge type regression estimators: A comparison. Surveys in Mathematics and its Applications, 3:111 – 122.

Batah, F. Sh., Gore, S.D., and Verma, M. R. 2008, Effect of Jackknifing on Various Ridge Type Estimators, Model Assisted Statistics and Applications, 3(3): 201 – 210.

Trenkler, G. and Toutenburg, H. (1990) Mean Square Error Matrix Comparisons between Biased Estimators: An Overview of Recent Results. Statistical Papers, 31: 165-179.

Farebrother R. W. 1976, Further results on the mean square error of ridge regression. J R Stat Soc B. 38 : 248 – 250.

Najarian, S., Arashi, M. and Kibria, B. M. G, (2013). A Simulation Study on Some Restricted Ridge Regression Estimators. Comm. Statist. Sim.Comp, 42:871-879.

Batah, F. Sh. 2013, Recovering Jackknife Ridge Regression Estimates from OLS Results, Journal of University of Anbar for Pure Science, 7(2): 1 – 8.

On Restricted Shrinkage Jackknife Biased Estimator for Restricted Linear Regression Model

References

References

Volume 17, Issue 2 - Issue Serial Number 2December 2023Page 245-253

Volume 17, Issue 2 - Issue Serial Number 2
December 2023
Page 245-253