Title :
A novel unified linear biased estimator
Author :
Yuanlong Yue ; Xin Zuo ; Lijun Wang
Author_Institution :
Dept. of Autom., China Univ. of Pet., Beijing, China
Abstract :
A novel unified biased estimator based on the linear transform matrix acting on the least-squares estimator (LSE) in canonical form is proposed for coping with multicollinearity problem and its properties are also discussed in this paper. We show that our new biased estimator is superior, in the mean squared error (MSE) sense, to the LSE. Ridge estimator, Liu estimator, etc. are viewed as a subclass of the class of the proposed estimator which is the linear transform of LSE. Finally, a numerical example widely used in the literatures is studies based on Monte Carlo simulation to show the behavior of the different estimators.
Keywords :
Monte Carlo methods; estimation theory; least squares approximations; matrix algebra; mean square error methods; transforms; LSE; Liu estimator; MSE; Monte Carlo simulation; canonical form; least-squares estimator; linear transform matrix; mean squared error; multicollinearity problem; ridge estimator; unified linear biased estimator; Automation; Covariance matrices; Mathematical model; Monte Carlo methods; Symmetric matrices; Transforms; Vectors;
Conference_Titel :
Control and Automation (ICCA), 2013 10th IEEE International Conference on
Conference_Location :
Hangzhou
Print_ISBN :
978-1-4673-4707-5
DOI :
10.1109/ICCA.2013.6564934
