New Stochastic Restricted Estimator: A Step Towards Improved Modeling in Linear Regression
DOI:
https://doi.org/10.62933/isj.v2i1.13Keywords:
Biased estimation, Linear convex combination, Liu estimator, Mixed estimator, Mean squared error matrixAbstract
Here, we propose a new convex linear combination estimator, called the New Mixed Estimator (NME), for multiple linear regression models with stochastic linear constraints on unknown parameters and multicollinearity between explanatory variables. The Ordinary Mixed Estimator (OME) and the Biased Stochastic Restricted Liu-type Estimator (SRLIT), two well-known estimators, are integrated to create the NME. Using Mean Square Error (MSE) as the main performance parameter, we examine the statistical characteristics of the NME and theoretically compare it to both OME and SRLIT to show its superiority. According to our research, the NME routinely performs better than the OME and SRLIT in terms of overall efficacy and statistical characteristics. Additionally, we provide a numerical example to clearly support these findings.
References
[1] Hoerl, A. E., Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. *Technometrics*, 12(1), 55-67.
[2] Baye, M. R., Parker, D. F. (1984). Combining ridge and principal component regression: A money demand illustration. *Communications in Statistics-Theory and Methods*, 13(2), 197-205.
[3] Liu, K. (1993). A new class of biased estimate in linear regression. *Communications in Statistics-Theory and Methods*, 22(2), 393-402.
[4] Kaçıranlar, S., Sakallıoğlu, S. (2001). Combining the Liu estimator and the principal component regression estimator. *Communications in Statistics-Theory and Methods*, 30(10), 2699-2705.
[5] Liu, K. (2003). Using Liu-type estimator to combat collinearity. *Communications in Statistics-Theory and Methods*, 32(5), 1009-1020.
[6] Liu, K. (2004). More on Liu-type estimator in linear regression. *Communications in Statistics-Theory and Methods*, 33(11), 2723-2733.
[7] Akdeniz, F., Kaçıranlar, S. (1995). On the almost unbiased generalized Liu estimator and unbiased estimation of the bias and MSE. *Communications in Statistics-Theory and Methods*, 24(7), 1789-1797.
[8] Akdeniz, F., Erol, H. (2003). Mean squared error matrix comparisons of some biased estimators in linear regression. *Communications in Statistics-Theory and Methods*, 32(12), 2389-2413.
[9] Massy, W. F. (1965). Principal components regression in exploratory statistical research. *Journal of the American Statistical Association*, 60(309), 234-256.
[10] Neter, J., Wasserman, W., Kutner, M. H. (1989). Applied Linear Regression Models (Vol. 2). Irwin Press.
[11] Özbey, F., Kaçıranlar, S. (2015). Evaluation of the predictive performance of the Liu estimator. *Communications in Statistics-Theory and Methods*, 44(10), 1981-1993.
[12] Arumairajan, S., Wijekoon, P. (2017). Modified almost unbiased Liu estimator in linear regression model. *Communications in Mathematics and Statistics*, 5, 261-276.
[13] Theil, H., Goldberger, A. S. (1992). On pure and mixed statistical estimation in economics. In H. Theil's Contributions to Economics and Econometrics: Econometric Theory and Methodology (pp. 317-332). Dordrecht: Springer Netherlands.
[14] Theil, H. (1963). On the use of incomplete prior information in regression analysis. *Journal of the American Statistical Association*, 58(302), 401-414.
[15] Alheety, M. I. N. (2020). New versions of Liu-type estimator in weighted and non-weighted mixed regression model. *Baghdad Science Journal*, 17(1 Suppl.), 0361-0361.
[16] Trenkler, G., Toutenburg, H. (1990). Mean squared error matrix comparisons between biased estimators—An overview of recent results. *Statistical Papers*, 31(1), 165-179.
[17] Rao, H., Toutenburg, H., Heumann, S.C. (2008). Linear Models and Generalizations: Least Squares and Alternatives. Springer-Verlag.
[18] Bashtian, M., Hassanzadeh, M., Arashi, M., Tabatabaey, S.M.M. (2011). Using improved estimation strategies to combat multicollinearity. *Journal of Statistical Computation and Simulation*, 81(12), 1773-1797.
[19] Dawoud, I., Eledum, H. (2024). New Stochastic Restricted Biased Regression Estimators. *Mathematics*, 13(1), 15.
[20] Alheety, M.I., Nayem, H.M., Kibria, B.M.G. (2025). An Unbiased Convex Estimator Depending on Prior Information for the Classical Linear Regression Model. *Stats*, 8(1), 16.
[21] Li, Y., Yang, H. (2010). A new stochastic mixed ridge estimator in linear regression model. *Statistical Papers*, 51, 315-323.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Dounia J. Al-Obaidi, Mustafa Alheety (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Licensed under a CC-BY license: https://creativecommons.org/licenses/by-nc-sa/4.0/
