| Adaptive Unified Biased Estimators of Parameters in Linear Model |
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| 引用本文： | HuYang Li-xingZhu. Adaptive Unified Biased Estimators of Parameters in Linear Model[J]. 应用数学学报(英文版), 2004, 20(3): 425-432. DOI: 10.1007/s10255-004-0181-z |
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| 作者姓名： | HuYang Li-xingZhu |
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| 作者单位： | Hu Yang~1 Li-xing Zhu~(2,3)1 College of Science,Chongqing University,chongqing 400044,China(E-mail:yh@cqu.edu.cn)2 Department of Statistics and Actuarial Science,The University of Hong Kong3 Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China |
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| 基金项目： | Supported by a grant from The Research Grants Council of Hong Kong HKU7181/02H.The authors wishes to thank the referees for the constructive comments |
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| 摘 要： | To tackle multi collinearity or ill-conditioned design matrices in linear models,adaptive biasedestimators such as the time-honored Stein estimator,the ridge and the principal component estimators havebeen studied intensively.To study when a biased estimator uniformly outperforms the least squares estimator,some sufficient conditions are proposed in the literature.In this paper,we propose a unified framework toformulate a class of adaptive biased estimators.This class includes all existing biased estimators and some newones.A sufficient condition for outperforming the least squares estimator is proposed.In terms of selectingparameters in the condition,we can obtain all double-type conditions in the literature.
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| 关 键 词： | 最少结算评估 线性方程模型 充分条件 统一适应性评估 |
| 收稿时间： | 2003-01-20 |
Adaptive Unified Biased Estimators of Parameters in Linear Model |
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| Hu?YangEmail author,Li-xing?Zhu. Adaptive Unified Biased Estimators of Parameters in Linear Model[J]. Acta Mathematicae Applicatae Sinica, 2004, 20(3): 425-432. DOI: 10.1007/s10255-004-0181-z |
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| Authors: | Hu?Yang author-information" > author-information__contact u-icon-before" > mailto:yh@cqu.edu.cn" title=" yh@cqu.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Li-xing?Zhu |
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| Affiliation: | (1) College of Science, Chongqing University, chongqing, 400044, China;(2) Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, Hong Kong;(3) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China |
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| Abstract: | To tackle multi collinearity or ill-conditioned design matrices in linear models,adaptive biasedestimators such as the time-honored Stein estimator,the ridge and the principal component estimators havebeen studied intensively.To study when a biased estimator uniformly outperforms the least squares estimator,some sufficient conditions are proposed in the literature.In this paper,we propose a unified framework toformulate a class of adaptive biased estimators.This class includes all existing biased estimators and some newones.A sufficient condition for outperforming the least squares estimator is proposed.In terms of selectingparameters in the condition,we can obtain all double-type conditions in the literature. |
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| Keywords: | Least squares estimator linear model sufficient coadition adaptive unified biased estimator |
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