NDLI: On Biased Estimation in Linear Models

Content Provider	IEEE Xplore Digital Library
Author	Zhi-Fu Wang Xian-Wei Yu Jing Zhang Na Li Wei Zhao Li Li
Copyright Year	2006
Description	Author affiliation: Bohai Univ., Liaoning (Zhi-Fu Wang; Xian-Wei Yu; Jing Zhang; Na Li; Wei Zhao; Li Li)
Abstract	Hoerl and Kennard introduced a class of biased estimators (ridge estimators) for the parameters in an ill-conditioned linear model. In this paper the ridge estimators are viewed as a subclass of linear transforms of the least squares estimators. An alternative class of estimators, labeled shrunken estimators is considered. It is shown that these estimators satisfy the admissibility condition proposed by Hoerl and Kennard. In addition, both the ridge estimators and shrunken estimators are derived as minimum norm estimators in the class of linear transforms of the least squares estimators. The former minimizes the Euclidean norm and the latter minimizes the design dependent norm. The class of estimators is obtained and the members of this class are shown to be stochastically shrunken estimators
Sponsorship	IEEE Syst., Man and Cybernetics Hebei Univ.
Starting Page	3671
Ending Page	3676
File Size	329298
Page Count	6
File Format	PDF
ISBN	1424400619
DOI	10.1109/ICMLC.2006.258624
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-08-13
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Least squares approximation Parameter estimation Vectors Mean square error methods Machine learning Cybernetics Multicollinearity ill-conditioning Biased Estimation Regression linear Models Ridge Estimation Shrunken Estimation Least squares
Content Type	Text
Resource Type	Article

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