Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 4 (2009), 155 -- 167## ON THE LIU AND ALMOST UNBIASED LIU ESTIMATORS IN THE PRESENCE OF MULTICOLLINEARITY WITH HETEROSCEDASTIC OR CORRELATED ERRORS

## M. I. Alheety and B. M. Golam Kibria

Abstract. This paper introduces a new biased estimator, namely, almost unbiased Liu estimator (AULE) of β for the multiple linear regression model with heteroscedastics and/or correlated errors and suffers from the problem of multicollinearity. The properties of the proposed estimator is discussed and the performance over the generalized least squares (GLS) estimator, ordinary ridge regression (ORR) estimator (Trenkler [20]), and Liu estimator (LE) (Kaçiranlar [10]) in terms of matrix mean square error criterion are investigated. The optimal values of d for Liu and almost unbiased Liu estimators have been obtained. Finally, a simulation study has been conducted which indicated that under certain conditions on d, the proposed estimator performed well compared to GLS, ORR and LE estimators.2000 Mathematics Subject Classification:62J05; 62F10.

Keywords:Bias, Linear Model; Liu Estimator; MSE; Multicollinearity; OLS; Simulation.

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Mustafa I. Alheety B. M. Golam Kibria Department of Mathematics Department of Mathematics and Statistics Alanbar University, Iraq Florida International University, Miami, FL 33199, USA. e-mail: alheety@yahoo.com e-mail: kibriag@fiu.edu