Modified Unbiased Optimal Estimator For Linear Regression Model

AL-jumaili, Hussein Ail; Alheety, Mustafa Ismail

doi:10.37652/juaps.2023.140832.1078

	Modified Unbiased Optimal Estimator For Linear Regression Model
Journal of University of Anbar for Pure Science
Article 36, Volume 17, Issue 2, December 2023, Pages 269-272 PDF (717.96 K)
Document Type: Research Paper
DOI: 10.37652/juaps.2023.140832.1078
Authors
Hussein Ail AL-jumaili^* ¹; Mustafa Ismail Alheety²
¹Department of Mathematics, College of education for pure science University of Anbar. Anbar. Iraq
²Department of Mathematics, College of education for pure science University of Anbar. Anbar. Iraq;
Abstract
Abstract In this paper, we propose a novel form of Generalized Unbiased Optimal Estimator where the explanatory variables are multicollinear. The proposed estimator's bias, variance, and mean square error matrix (MSE) are calculated. The MSE criterion is used to compare the performance of this estimator against that of other estimators. Finally, a numerical example is examined to understand more about the new estimator's performance. Keywords : Almost Unbiased Ridge Estimator , Modified Almost Unbiased Two-Parameter , Generalized Unbiased Estimator , Mean Squared Error, 1.Introdeuction Consider the following multiple linear regression model Y=Xβ+ϵ (1) Where X is an n×p known matrix of dependent variable, Y is an n×1 vector of remarks the dependent variable, β is an p×1 vector of unknown regression coefficients, and ϵ is an n×1 vector of errors term disturbance, such that E(ϵ ) = 0 and V(ϵ ) = σ^2 I . The ordinary least square (OLS) estimator of β in model (1) is an given by, β ̂ = S^(-1) X^' Y
Keywords
matrx,,; ,،variance,,; ,،mean squre,,; ,،multicollinear

References
Stein,( 1956), Inadmissibility of the usual estimator for mean of multivariate normal distribution, Proceedings of the Third Berkley Symposium on Mathematical and Statistics Probability, J. Neyman, ed., Vol. 1, pp. 197–206. E. Hoerl and R.W. Kennard, (1970), Ridge regression: Biased estimation for non-orthogonal problems, Technometrics . Liu, (1993), A new class of biased estimate in linear regression, Commmun. Stat. Theory Methods. Liu, K. (1993) A New Class of Biased Estimate in Linear Regression. Communications in Statistics Theory and Methods, 22, 393-402. B., Chaubey. Y.P. and Dwivedi, T.D. (1986) An Almost Unbiased Ridge Estimator. Sankhya: The Indian Journal of Statistics B, 48, 342-346. Akdeniz, F. and Kaçiranlar, S. (1995) On the Almost Unbiased Generalized Liu Estimator and Unbiased Estimation of the Bias and MSE. Communications in Statistics Theory and Methods, 34, 1789-1797. Lukman, A. F., Adewuyi, E., Oladejo, N., & Olukayode, A. (2019, November). Modified Almost Unbiased Two-Parameter Estimator in linear regression model. In IOP Conference Series: Materials Science and Engineering .‏ Özkale, M. R., & Kaçiranlar, S. (2007). The restricted and unrestricted two-parameter estimators. Communications in Statistics Theory and Methods. Wang, S. G., Shen, C. B., Long, K., Zhang, T., Wang, F. H., & Zhang, Z. D. (2006). The electrochemical corrosion of bulk nanocrystalline ingot iron in acidic sulfate solution. The Journal of Physical Chemistry B. Trenkler, G., & Toutenburg, H. (1990). Mean squared error matrix comparisons between biased estimators—An overview of recent results. Statistical papers, 31(1), 165-179.‏ R. Rao, H. Toutenburg, and S.C. Heumann, (2008) Linear Models and Generalizations: Least Squares and Alternatives, Springer-Verlag, New York. Woods, H. H. Steinour, and H. R. Starke, (1932) “Effect of composition of Portland cement on heat evolved during hardening,” Industrial and Engineering Chemistry. Alheety, Mustafa Ismaeel Naif. (2020) "New versions of liu-type estimator in weighted and non-weighted mixed regression model." Baghdad Science Journal 17.1 (Suppl): 0361-0361 Ohtani, K., (1986). On small sample properties of the almost unbiased generalized ridge estimator. Communications in Statistics-Theory and Methods, 15, 1571-1578. Rao, C.R. and Touterburg, H. (1995) Linear Models, Least Squares and Alternatives. Springer Verlag.
Statistics Article View: 796 PDF Download: 288