Modified Unbiased Optimal Estimator For Linear Regression Model

• Published in: مجلة جامعة الانبار للعلوم الصرفة Vol. 17; no. 2; pp. 269 - 272
• Main Authors: Hussein AL-jumaili, Mustafa Alheety
• Format: Journal Article
• Language: English
• Published: University of Anbar 01.12.2023
• Subjects: matrx; mean squre; multicollinear; variance
• ISSN: 1991-8941; 2706-6703
• DOI: 10.37652/juaps.2023.140832.1078

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.IntrodeuctionConsider the following multiple linear regression modelY=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