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Adaptive Unified Biased Estimators of Parameters in Linear Model

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Abstract

To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been 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 to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.

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Authors and Affiliations

  1. College of Science, Chongqing University, chongqing, 400044, China

    Hu Yang

  2. Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, Hong Kong

    Li-xing Zhu

  3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Li-xing Zhu

Authors
  1. Hu Yang
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  2. Li-xing Zhu
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Correspondence to Hu Yang.

Additional information

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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Yang, H., Zhu, Lx. Adaptive Unified Biased Estimators of Parameters in Linear Model. Acta Mathematicae Applicatae Sinica, English Series 20, 425–432 (2004). https://doi.org/10.1007/s10255-004-0181-z

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  • DOI: https://doi.org/10.1007/s10255-004-0181-z

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