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On the restricted almost unbiased estimators in linear regression

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In this paper, the restricted almost unbiased ridge regression estimator and restricted almost unbiased Liu estimator are introduced for the vector of parameters in a multiple linear regression model with linear restrictions. The bias, variance matrices and mean square error (MSE) of the proposed estimators are derived and compared. It is shown that the proposed estimators will have smaller quadratic bias but larger variance than the corresponding competitors in literatures. However, they will respectively outperform the latter according to the MSE criterion under certain conditions. Finally, a simulation study and a numerical example are given to illustrate some of the theoretical results.
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Keywords: almost unbiased Liu estimator; almost unbiased ridge estimator; linear restrictions; mean square error; multicollinearity

Document Type: Research Article

Affiliations: Department of Statistics and Actuarial Science, Chongqing University, People's Republic of China

Publication date: March 1, 2011

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